digraph physicsDerivation { 
overlap = false;
label="derivation: upper limit on velocity in condensed matter
https://allofphysiscs.com";
fontsize=12;
0007232268 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0007232268 -> generated_expression_4560648264_f102e973d7bd5432e00c65a7e1b3c285357f081c558077f7ac051768ece1a74c;
generated_expression_4560648264_f102e973d7bd5432e00c65a7e1b3c285357f081c558077f7ac051768ece1a74c [shape=ellipse, color=black,label="",image="/code/static/generated_expression_4560648264_f102e973d7bd5432e00c65a7e1b3c285357f081c558077f7ac051768ece1a74c.png",labelloc=b];
0006342896 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0006342896 -> generated_expression_9376481176_fc2e4217a76eaac6b9cc0b41a0404279f0df5aaf80dee6e2accdcb0609e5f60b;
generated_expression_9376481176_fc2e4217a76eaac6b9cc0b41a0404279f0df5aaf80dee6e2accdcb0609e5f60b [shape=ellipse, color=black,label="",image="/code/static/generated_expression_9376481176_fc2e4217a76eaac6b9cc0b41a0404279f0df5aaf80dee6e2accdcb0609e5f60b.png",labelloc=b];
0009182821 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_dropnondominantterm.png",labelloc=b];
generated_expression_4560648264_f102e973d7bd5432e00c65a7e1b3c285357f081c558077f7ac051768ece1a74c -> 0009182821;
generated_expression_4560648264_f102e973d7bd5432e00c65a7e1b3c285357f081c558077f7ac051768ece1a74c [shape=ellipse, color=black,label="",image="/code/static/generated_expression_4560648264_f102e973d7bd5432e00c65a7e1b3c285357f081c558077f7ac051768ece1a74c.png",labelloc=b];
0009182821 -> generated_expression_6504442697_4d78d7f44ee89a675f7d8e8bedaebed554b9709d81542b6dc34159670e93f267;
generated_expression_6504442697_4d78d7f44ee89a675f7d8e8bedaebed554b9709d81542b6dc34159670e93f267 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_6504442697_4d78d7f44ee89a675f7d8e8bedaebed554b9709d81542b6dc34159670e93f267.png",labelloc=b];
generated_feed_9674924517_630a8364d4a865e7a4a951bf757964ac6a20c43f039602870a16bfbdc728dc12 -> 0009182821;
generated_feed_9674924517_630a8364d4a865e7a4a951bf757964ac6a20c43f039602870a16bfbdc728dc12 [shape=box, color=red,label="",image="/code/static/generated_feed_9674924517_630a8364d4a865e7a4a951bf757964ac6a20c43f039602870a16bfbdc728dc12.png",labelloc=b];
0007117931 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_substituteLHSofexpr1intoexpr2.png",labelloc=b];
generated_expression_6504442697_4d78d7f44ee89a675f7d8e8bedaebed554b9709d81542b6dc34159670e93f267 -> 0007117931;
generated_expression_6504442697_4d78d7f44ee89a675f7d8e8bedaebed554b9709d81542b6dc34159670e93f267 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_6504442697_4d78d7f44ee89a675f7d8e8bedaebed554b9709d81542b6dc34159670e93f267.png",labelloc=b];
generated_expression_9376481176_fc2e4217a76eaac6b9cc0b41a0404279f0df5aaf80dee6e2accdcb0609e5f60b -> 0007117931;
generated_expression_9376481176_fc2e4217a76eaac6b9cc0b41a0404279f0df5aaf80dee6e2accdcb0609e5f60b [shape=ellipse, color=black,label="",image="/code/static/generated_expression_9376481176_fc2e4217a76eaac6b9cc0b41a0404279f0df5aaf80dee6e2accdcb0609e5f60b.png",labelloc=b];
0007117931 -> generated_expression_8090924099_61b6d65f700a7b9d51503a4b4b4fe2210304d40ef540831f69dac4574404b49e;
generated_expression_8090924099_61b6d65f700a7b9d51503a4b4b4fe2210304d40ef540831f69dac4574404b49e [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8090924099_61b6d65f700a7b9d51503a4b4b4fe2210304d40ef540831f69dac4574404b49e.png",labelloc=b];
0006394441 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0006394441 -> generated_expression_8908736791_83bee3c6e9f3c228901a1a34e42061239c6de59d026c7d65069feaaf0c2f856a;
generated_expression_8908736791_83bee3c6e9f3c228901a1a34e42061239c6de59d026c7d65069feaaf0c2f856a [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8908736791_83bee3c6e9f3c228901a1a34e42061239c6de59d026c7d65069feaaf0c2f856a.png",labelloc=b];
0006240791 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_multiplybothsidesby.png",labelloc=b];
generated_expression_8908736791_83bee3c6e9f3c228901a1a34e42061239c6de59d026c7d65069feaaf0c2f856a -> 0006240791;
generated_expression_8908736791_83bee3c6e9f3c228901a1a34e42061239c6de59d026c7d65069feaaf0c2f856a [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8908736791_83bee3c6e9f3c228901a1a34e42061239c6de59d026c7d65069feaaf0c2f856a.png",labelloc=b];
0006240791 -> generated_expression_8688588981_5c466683b0411f300b15bfab2af3921911fc8619e9f4daa2999d6b3ded543c7d;
generated_expression_8688588981_5c466683b0411f300b15bfab2af3921911fc8619e9f4daa2999d6b3ded543c7d [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8688588981_5c466683b0411f300b15bfab2af3921911fc8619e9f4daa2999d6b3ded543c7d.png",labelloc=b];
generated_feed_2397692197_7b48479868582d730bbde34ef5c13507cb89e1a25c0964d45121e2032dd8b708 -> 0006240791;
generated_feed_2397692197_7b48479868582d730bbde34ef5c13507cb89e1a25c0964d45121e2032dd8b708 [shape=box, color=red,label="",image="/code/static/generated_feed_2397692197_7b48479868582d730bbde34ef5c13507cb89e1a25c0964d45121e2032dd8b708.png",labelloc=b];
0003423374 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_substituteRHSofexpr1intoexpr2.png",labelloc=b];
generated_expression_8090924099_61b6d65f700a7b9d51503a4b4b4fe2210304d40ef540831f69dac4574404b49e -> 0003423374;
generated_expression_8090924099_61b6d65f700a7b9d51503a4b4b4fe2210304d40ef540831f69dac4574404b49e [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8090924099_61b6d65f700a7b9d51503a4b4b4fe2210304d40ef540831f69dac4574404b49e.png",labelloc=b];
generated_expression_8688588981_5c466683b0411f300b15bfab2af3921911fc8619e9f4daa2999d6b3ded543c7d -> 0003423374;
generated_expression_8688588981_5c466683b0411f300b15bfab2af3921911fc8619e9f4daa2999d6b3ded543c7d [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8688588981_5c466683b0411f300b15bfab2af3921911fc8619e9f4daa2999d6b3ded543c7d.png",labelloc=b];
0003423374 -> generated_expression_7837519722_74bb08d2e9c1547693f16b4d603e970f70c4eac864d7fb7f40917e5ba296a59c;
generated_expression_7837519722_74bb08d2e9c1547693f16b4d603e970f70c4eac864d7fb7f40917e5ba296a59c [shape=ellipse, color=black,label="",image="/code/static/generated_expression_7837519722_74bb08d2e9c1547693f16b4d603e970f70c4eac864d7fb7f40917e5ba296a59c.png",labelloc=b];
0009057006 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_dropnondominantterm.png",labelloc=b];
generated_expression_7837519722_74bb08d2e9c1547693f16b4d603e970f70c4eac864d7fb7f40917e5ba296a59c -> 0009057006;
generated_expression_7837519722_74bb08d2e9c1547693f16b4d603e970f70c4eac864d7fb7f40917e5ba296a59c [shape=ellipse, color=black,label="",image="/code/static/generated_expression_7837519722_74bb08d2e9c1547693f16b4d603e970f70c4eac864d7fb7f40917e5ba296a59c.png",labelloc=b];
0009057006 -> generated_expression_9854442418_e85d22f64ace22930e557a7d12a1913dd57f633d944b4d1f82d95a0808fe5b9e;
generated_expression_9854442418_e85d22f64ace22930e557a7d12a1913dd57f633d944b4d1f82d95a0808fe5b9e [shape=ellipse, color=black,label="",image="/code/static/generated_expression_9854442418_e85d22f64ace22930e557a7d12a1913dd57f633d944b4d1f82d95a0808fe5b9e.png",labelloc=b];
generated_feed_3685779219_8153097e94bc632fac71eb9fd8f54e891bdd189509c1d617641529a59d976887 -> 0009057006;
generated_feed_3685779219_8153097e94bc632fac71eb9fd8f54e891bdd189509c1d617641529a59d976887 [shape=box, color=red,label="",image="/code/static/generated_feed_3685779219_8153097e94bc632fac71eb9fd8f54e891bdd189509c1d617641529a59d976887.png",labelloc=b];
0002951905 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0002951905 -> generated_expression_1556389363_0fbb919321313dcf3a7d5c80b09b963a87f40a60e00682c4bf97afc6910680db;
generated_expression_1556389363_0fbb919321313dcf3a7d5c80b09b963a87f40a60e00682c4bf97afc6910680db [shape=ellipse, color=black,label="",image="/code/static/generated_expression_1556389363_0fbb919321313dcf3a7d5c80b09b963a87f40a60e00682c4bf97afc6910680db.png",labelloc=b];
0005093643 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareassumption.png",labelloc=b];
0005093643 -> generated_expression_4107032818_5c07dc72d3f66d189771e42cd2a2ea2f1eed2377c152b0d6bd0c17d709387064;
generated_expression_4107032818_5c07dc72d3f66d189771e42cd2a2ea2f1eed2377c152b0d6bd0c17d709387064 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_4107032818_5c07dc72d3f66d189771e42cd2a2ea2f1eed2377c152b0d6bd0c17d709387064.png",labelloc=b];
0001346919 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0001346919 -> generated_expression_8106885760_5d1b7d39abac59a761f8cc773c18804eef05df2375d87e0b47dc25b12278e905;
generated_expression_8106885760_5d1b7d39abac59a761f8cc773c18804eef05df2375d87e0b47dc25b12278e905 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8106885760_5d1b7d39abac59a761f8cc773c18804eef05df2375d87e0b47dc25b12278e905.png",labelloc=b];
0001452028 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_multiplybothsidesby.png",labelloc=b];
generated_expression_8106885760_5d1b7d39abac59a761f8cc773c18804eef05df2375d87e0b47dc25b12278e905 -> 0001452028;
generated_expression_8106885760_5d1b7d39abac59a761f8cc773c18804eef05df2375d87e0b47dc25b12278e905 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8106885760_5d1b7d39abac59a761f8cc773c18804eef05df2375d87e0b47dc25b12278e905.png",labelloc=b];
0001452028 -> generated_expression_5838268428_1e1c8acdb8ba4fe3533f70c470bc213af371e9e94e963805c664c95f356dbee0;
generated_expression_5838268428_1e1c8acdb8ba4fe3533f70c470bc213af371e9e94e963805c664c95f356dbee0 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5838268428_1e1c8acdb8ba4fe3533f70c470bc213af371e9e94e963805c664c95f356dbee0.png",labelloc=b];
generated_feed_8857931498_2e7d2c03a9507ae265ecf5b5356885a53393a2029d241394997265a1a25aefc6 -> 0001452028;
generated_feed_8857931498_2e7d2c03a9507ae265ecf5b5356885a53393a2029d241394997265a1a25aefc6 [shape=box, color=red,label="",image="/code/static/generated_feed_8857931498_2e7d2c03a9507ae265ecf5b5356885a53393a2029d241394997265a1a25aefc6.png",labelloc=b];
0005023393 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_substituteLHSofexpr1intoexpr2.png",labelloc=b];
generated_expression_1556389363_0fbb919321313dcf3a7d5c80b09b963a87f40a60e00682c4bf97afc6910680db -> 0005023393;
generated_expression_1556389363_0fbb919321313dcf3a7d5c80b09b963a87f40a60e00682c4bf97afc6910680db [shape=ellipse, color=black,label="",image="/code/static/generated_expression_1556389363_0fbb919321313dcf3a7d5c80b09b963a87f40a60e00682c4bf97afc6910680db.png",labelloc=b];
generated_expression_4107032818_5c07dc72d3f66d189771e42cd2a2ea2f1eed2377c152b0d6bd0c17d709387064 -> 0005023393;
generated_expression_4107032818_5c07dc72d3f66d189771e42cd2a2ea2f1eed2377c152b0d6bd0c17d709387064 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_4107032818_5c07dc72d3f66d189771e42cd2a2ea2f1eed2377c152b0d6bd0c17d709387064.png",labelloc=b];
0005023393 -> generated_expression_3291685884_bac49459b1838aff1c41a9ff201fa9b189ac604c9883435dfc067a96c379c57a;
generated_expression_3291685884_bac49459b1838aff1c41a9ff201fa9b189ac604c9883435dfc067a96c379c57a [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3291685884_bac49459b1838aff1c41a9ff201fa9b189ac604c9883435dfc067a96c379c57a.png",labelloc=b];
0007588540 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_substituteLHSofexpr1intoexpr2.png",labelloc=b];
generated_expression_9854442418_e85d22f64ace22930e557a7d12a1913dd57f633d944b4d1f82d95a0808fe5b9e -> 0007588540;
generated_expression_9854442418_e85d22f64ace22930e557a7d12a1913dd57f633d944b4d1f82d95a0808fe5b9e [shape=ellipse, color=black,label="",image="/code/static/generated_expression_9854442418_e85d22f64ace22930e557a7d12a1913dd57f633d944b4d1f82d95a0808fe5b9e.png",labelloc=b];
generated_expression_3291685884_bac49459b1838aff1c41a9ff201fa9b189ac604c9883435dfc067a96c379c57a -> 0007588540;
generated_expression_3291685884_bac49459b1838aff1c41a9ff201fa9b189ac604c9883435dfc067a96c379c57a [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3291685884_bac49459b1838aff1c41a9ff201fa9b189ac604c9883435dfc067a96c379c57a.png",labelloc=b];
0007588540 -> generated_expression_3935058307_daf3c4d19786f1f87ec29f9c2384570dab60c1a307a4a37635ef551659743cb2;
generated_expression_3935058307_daf3c4d19786f1f87ec29f9c2384570dab60c1a307a4a37635ef551659743cb2 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3935058307_daf3c4d19786f1f87ec29f9c2384570dab60c1a307a4a37635ef551659743cb2.png",labelloc=b];
0005522705 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_simplify.png",labelloc=b];
generated_expression_3935058307_daf3c4d19786f1f87ec29f9c2384570dab60c1a307a4a37635ef551659743cb2 -> 0005522705;
generated_expression_3935058307_daf3c4d19786f1f87ec29f9c2384570dab60c1a307a4a37635ef551659743cb2 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3935058307_daf3c4d19786f1f87ec29f9c2384570dab60c1a307a4a37635ef551659743cb2.png",labelloc=b];
0005522705 -> generated_expression_9640720571_180c538bd2f94ecddb6f5fc8834e94b576bfba2cead320afb8868dd7d93e6a14;
generated_expression_9640720571_180c538bd2f94ecddb6f5fc8834e94b576bfba2cead320afb8868dd7d93e6a14 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_9640720571_180c538bd2f94ecddb6f5fc8834e94b576bfba2cead320afb8868dd7d93e6a14.png",labelloc=b];
0009573616 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_substituteLHSofexpr1intoexpr2.png",labelloc=b];
generated_expression_9640720571_180c538bd2f94ecddb6f5fc8834e94b576bfba2cead320afb8868dd7d93e6a14 -> 0009573616;
generated_expression_9640720571_180c538bd2f94ecddb6f5fc8834e94b576bfba2cead320afb8868dd7d93e6a14 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_9640720571_180c538bd2f94ecddb6f5fc8834e94b576bfba2cead320afb8868dd7d93e6a14.png",labelloc=b];
generated_expression_5838268428_1e1c8acdb8ba4fe3533f70c470bc213af371e9e94e963805c664c95f356dbee0 -> 0009573616;
generated_expression_5838268428_1e1c8acdb8ba4fe3533f70c470bc213af371e9e94e963805c664c95f356dbee0 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5838268428_1e1c8acdb8ba4fe3533f70c470bc213af371e9e94e963805c664c95f356dbee0.png",labelloc=b];
0009573616 -> generated_expression_5789289057_e2a1776b18e19689a57b7176fefbe921b8f46dba3444a40e70f6f88254e7d899;
generated_expression_5789289057_e2a1776b18e19689a57b7176fefbe921b8f46dba3444a40e70f6f88254e7d899 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5789289057_e2a1776b18e19689a57b7176fefbe921b8f46dba3444a40e70f6f88254e7d899.png",labelloc=b];
0008867459 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0008867459 -> generated_expression_5646314683_0602555557c3b2004a9e6d53a65f7a6fae152b78c36fb69cff96d8dd79bde684;
generated_expression_5646314683_0602555557c3b2004a9e6d53a65f7a6fae152b78c36fb69cff96d8dd79bde684 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5646314683_0602555557c3b2004a9e6d53a65f7a6fae152b78c36fb69cff96d8dd79bde684.png",labelloc=b];
0004186156 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_substituteLHSofexpr1intoexpr2.png",labelloc=b];
generated_expression_5789289057_e2a1776b18e19689a57b7176fefbe921b8f46dba3444a40e70f6f88254e7d899 -> 0004186156;
generated_expression_5789289057_e2a1776b18e19689a57b7176fefbe921b8f46dba3444a40e70f6f88254e7d899 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5789289057_e2a1776b18e19689a57b7176fefbe921b8f46dba3444a40e70f6f88254e7d899.png",labelloc=b];
generated_expression_5646314683_0602555557c3b2004a9e6d53a65f7a6fae152b78c36fb69cff96d8dd79bde684 -> 0004186156;
generated_expression_5646314683_0602555557c3b2004a9e6d53a65f7a6fae152b78c36fb69cff96d8dd79bde684 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_5646314683_0602555557c3b2004a9e6d53a65f7a6fae152b78c36fb69cff96d8dd79bde684.png",labelloc=b];
0004186156 -> generated_expression_2897612567_65f2427d7015d0f13f85a6b618a29d67873bd953fbfec3f3223a3204ab81e9f1;
generated_expression_2897612567_65f2427d7015d0f13f85a6b618a29d67873bd953fbfec3f3223a3204ab81e9f1 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2897612567_65f2427d7015d0f13f85a6b618a29d67873bd953fbfec3f3223a3204ab81e9f1.png",labelloc=b];
0003709291 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_maximumofexpression.png",labelloc=b];
generated_expression_2897612567_65f2427d7015d0f13f85a6b618a29d67873bd953fbfec3f3223a3204ab81e9f1 -> 0003709291;
generated_expression_2897612567_65f2427d7015d0f13f85a6b618a29d67873bd953fbfec3f3223a3204ab81e9f1 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2897612567_65f2427d7015d0f13f85a6b618a29d67873bd953fbfec3f3223a3204ab81e9f1.png",labelloc=b];
0003709291 -> generated_expression_7701249282_9fbb03c94e0486789ded3d2c438fdf2a52d1c5582fd43324dc51dcaeeb74ac9c;
generated_expression_7701249282_9fbb03c94e0486789ded3d2c438fdf2a52d1c5582fd43324dc51dcaeeb74ac9c [shape=ellipse, color=black,label="",image="/code/static/generated_expression_7701249282_9fbb03c94e0486789ded3d2c438fdf2a52d1c5582fd43324dc51dcaeeb74ac9c.png",labelloc=b];
generated_feed_6259833695_559aead08264d5795d3909718cdd05abd49572e84fe55590eef31a88a08fdffd -> 0003709291;
generated_feed_6259833695_559aead08264d5795d3909718cdd05abd49572e84fe55590eef31a88a08fdffd [shape=box, color=red,label="",image="/code/static/generated_feed_6259833695_559aead08264d5795d3909718cdd05abd49572e84fe55590eef31a88a08fdffd.png",labelloc=b];
0004663270 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declarefinalexpression.png",labelloc=b];
generated_expression_7701249282_9fbb03c94e0486789ded3d2c438fdf2a52d1c5582fd43324dc51dcaeeb74ac9c -> 0004663270;
generated_expression_7701249282_9fbb03c94e0486789ded3d2c438fdf2a52d1c5582fd43324dc51dcaeeb74ac9c [shape=ellipse, color=black,label="",image="/code/static/generated_expression_7701249282_9fbb03c94e0486789ded3d2c438fdf2a52d1c5582fd43324dc51dcaeeb74ac9c.png",labelloc=b];
}