[
"LHS of expr 1 equals LHS of expr 2",
"RHS of expr 1 equals RHS of expr 2",
"X cross both sides by",
"X dot both sides",
"add X to both sides",
"add expr 1 to expr 2",
"add zero to LHS",
"add zero to RHS",
"apply divergence",
"apply function to both sides of expression",
"apply gradient to scalar function",
"apply operator to bra",
"apply operator to ket",
"assume N dimensions",
"both sides cross X",
"both sides dot X",
"boundary condition",
"boundary condition for expr",
"change five variables in expr",
"change four variables in expr",
"change six variables in expr",
"change three variables in expr",
"change two variables in expr",
"change variable X to Y",
"claim LHS equals RHS",
"claim expr 1 equals expr 2",
"combine like terms",
"conjugate both sides",
"conjugate function X",
"conjugate transpose both sides",
"declare assumption",
"declare final expr",
"declare guess solution",
"declare identity",
"declare initial expr",
"differentiate with respect to",
"distribute conjugate to factors",
"distribute conjugate transpose to factors",
"divide both sides by",
"divide expr 1 by expr 2",
"drop non-dominant term",
"evaluate definite integral",
"expand LHS",
"expand RHS",
"expand integrand",
"expand magnitude to conjugate",
"expr 1 is equivalent to expr 2 under the condition",
"expr 1 is true under condition expr 2",
"factor out X",
"factor out X from LHS",
"factor out X from RHS",
"function is even",
"function is odd",
"indefinite integral over",
"indefinite integrate LHS over",
"indefinite integrate RHS over",
"indefinite integration",
"integrate",
"integrate over from to",
"make expr power",
"maximum of expr",
"multiply LHS by unity",
"multiply RHS by unity",
"multiply both sides by",
"multiply expr 1 by expr 2",
"normalization condition",
"partially differentiate with respect to",
"raise both sides to power",
"replace constant with value",
"replace curl with LeviCevita summation contravariant",
"replace scalar with vector",
"replace summation notation with vector notation",
"select imaginary parts",
"select real parts",
"separate three vector components",
"separate two vector components",
"separate vector into two trigonometric ratios",
"simplify",
"solve for X",
"square root both sides",
"substitute LHS of expr 1 into expr 2",
"substitute LHS of five expressions into expr",
"substitute LHS of four expressions into expr",
"substitute LHS of six expressions into expr",
"substitute LHS of three expressions into expr",
"substitute LHS of two expressions into expr",
"substitute RHS of expr 1 into expr 2",
"subtract X from both sides",
"subtract expr 1 from expr 2",
"sum exponents",
"sum exponents LHS",
"sum exponents RHS",
"swap LHS with RHS",
"take curl of both sides"
]