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lect04a
hw review; proofs
Show: if n is even, then n+1 is odd.
1. n is even premise (NB: n is arbitrary)
2. ∃k.(n=2k) def'n even
3. n=2k existential instantiation (NB k is not arbitrary)
4. ∀z.∀y.(z+1/2 &neq; y) th'm: no integers differ by less than 1.
5. ∀y.(k+1/2 &neq; y) universal instantiaion[z/k], line 4,
4. ¬∃m.(k+1/2 = m) by def'n of integer; (m arbitrary)
5. ¬∃m.(2k+1 = 2m) line4 + multiply equals by equals
6. ¬∃m.( n+1 = 2m) line 3 + subst equals for equals.
7. ¬(n+1 is even) by line15 + def'n of even
8. n+1 is odd by line16 + def'n of odd
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