MATH.11:12 - Relations

• MATH.1 constructs permitted paths and retains intermediate state; MATH.4 constructs witnesses by induction. This pattern constructs a preserved function and uses induction to obtain its consequence.
• MATH.2 forms identifications under retained operations. Equal invariant values give a possible identification, whose adequacy for another operation remains a separate question.
• MATH.5 extends a supplied generator assignment through composites. This method instead solves for an assignment that transformations preserve.
• MATH.7 transports an expression with its structure through a bijection. MATH.8 generates solution orbits; an invariant can rule out membership but need not distinguish all orbits.
• B.5.RA recovers the resulting argument; B.5.RR revises its affected dependencies; B.5.QD develops the next question from its obstruction or formula.
• C.29 connects the mathematical result to another subject. C.11.DUA helps decide whether a larger invariant search would change the next useful action.