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A comment on Terence Tao, "Machine Assisted Proof" [video]. Parent comment
Induction is just set membership. Every inductive proof looks like this:
1. There's a set, S.
2. There's a scalar value, e, in S.
3. e has property p.
4. There is a function, f, from S to S.
5. f preserves property p.
6. Every element of S can be reached from e by repeated application of f. (Often because S is defined to consist of e plus f(x) for any x in S.)
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7. Therefore, every element of S has property p.
Induction is just set membership. Every inductive proof looks like this:
1. There's a set, S.
2. There's a scalar value, e, in S.
3. e has property p.
4. There is a function, f, from S to S.
5. f preserves property p.
6. Every element of S can be reached from e by repeated application of f. (Often because S is defined to consist of e plus f(x) for any x in S.)
---------
7. Therefore, every element of S has property p.