Prove:
(Proposition (commutativity of addition): + = ) ,
under the assumptions:
(Proposition (15): 15) ,
(Proposition (20): 20) ,
(Definition (addition): 1) ,
(Definition (addition): 2) .
We prove () by induction on .
Induction Base:
(1) .
We take in () all variables arbitrary but fixed and prove:
(4) .
A proof by simplification of () works.
Simplification of the lhs term:
= by ()
⌋
Simplification of the rhs term:
= by ()
⌋
Induction Step:
Induction Hypothesis:
(2)
Induction Conclusion:
(3) .
We take in () all variables arbitrary but fixed and prove:
(5) .
A proof by simplification of () works.
Simplification of the lhs term:
= by ()
= by ()
⌋
Simplification of the rhs term:
= by ()
⌋
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