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abstract:
reference:

step	inference rule	input	feed	output	validity (as per SymPy)
1	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			5900595848 $k=\frac{\omega}{v}$	no validation is available for declarations
6	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	0404050504 $\lambda=\frac{v}{f}$ 3131111133 $T=1 / f$		1293923844 $\lambda=v T$	LHS diff is -pdg0001115 + pdg0009491 RHS diff is -pdg0001357*pdg0009491 + 1/pdg0004201
2	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			0404050504 $\lambda=\frac{v}{f}$	no validation is available for declarations
5	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	5900595848 $k=\frac{\omega}{v}$ 3132131132 $\omega=\frac{2\pi}{T}$		0934990943 $k=\frac{2 \pi}{v T}$	LHS diff is pdg0002321 - pdg0005321 RHS diff is 2pdg0003141(pdg0001357 - 1)/(pdg0001357*pdg0009491)
8	ID: 111182; multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	3131111133 $T=1 / f$	0005749291 $f$	2131616531 $T f=1$	LHS arithmetic error. Diff: pdg0009491*(-pdg0004201 + pdg0006235)
3	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			3131211131 $\omega=2 \pi f$	no validation is available for declarations
11	ID: 111341; declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\\ref{eq:#1} is one of the final equations.	3121513111 $k=\frac{2 \pi}{\lambda}$			no validation is available for declarations
7	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	1293923844 $\lambda=v T$ 0934990943 $k=\frac{2 \pi}{v T}$		3121513111 $k=\frac{2 \pi}{\lambda}$	valid
4	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			3131111133 $T=1 / f$	no validation is available for declarations
9	ID: 111975; divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	2131616531 $T f=1$	0008837284 $T$	2113211456 $f=1/T$	valid
10	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	3131211131 $\omega=2 \pi f$ 2113211456 $f=1/T$		3132131132 $\omega=\frac{2\pi}{T}$	LHS diff is -pdg0002321 + pdg0004201 RHS diff is (1 - 2*pdg0003141)/pdg0009491

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timing of Neo4j queries:

0.006 seconds for pdg_app/to_review_derivation: node_properties, derivation1865941
0.009 seconds for compute/get_dict_of_steps_in_derivation: steps_in_this_derivation3350419
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step	inference rule	input	feed	output	validity (as per SymPy)
1	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			5900595848 \(k=\frac{\omega}{v}\)	no validation is available for declarations
6	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	0404050504 \(\lambda=\frac{v}{f}\) 3131111133 \(T=1 / f\)		1293923844 \(\lambda=v T\)	LHS diff is -pdg0001115 + pdg0009491 RHS diff is -pdg0001357*pdg0009491 + 1/pdg0004201
2	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			0404050504 \(\lambda=\frac{v}{f}\)	no validation is available for declarations
5	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	5900595848 \(k=\frac{\omega}{v}\) 3132131132 \(\omega=\frac{2\pi}{T}\)		0934990943 \(k=\frac{2 \pi}{v T}\)	LHS diff is pdg0002321 - pdg0005321 RHS diff is 2pdg0003141(pdg0001357 - 1)/(pdg0001357*pdg0009491)
8	ID: 111182; multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	3131111133 \(T=1 / f\)	0005749291 \(f\)	2131616531 \(T f=1\)	LHS arithmetic error. Diff: pdg0009491*(-pdg0004201 + pdg0006235)
3	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			3131211131 \(\omega=2 \pi f\)	no validation is available for declarations
11	ID: 111341; declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\\ref{eq:#1} is one of the final equations.	3121513111 \(k=\frac{2 \pi}{\lambda}\)			no validation is available for declarations
7	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	1293923844 \(\lambda=v T\) 0934990943 \(k=\frac{2 \pi}{v T}\)		3121513111 \(k=\frac{2 \pi}{\lambda}\)	valid
4	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			3131111133 \(T=1 / f\)	no validation is available for declarations
9	ID: 111975; divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	2131616531 \(T f=1\)	0008837284 \(T\)	2113211456 \(f=1/T\)	valid
10	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	3131211131 \(\omega=2 \pi f\) 2113211456 \(f=1/T\)		3132131132 \(\omega=\frac{2\pi}{T}\)	LHS diff is -pdg0002321 + pdg0004201 RHS diff is (1 - 2*pdg0003141)/pdg0009491