Theorem splitopt ≪ | index | src | ≫

theorem splitopt (G: wff) (a: nat) (p: wff):
  $ G -> a = 0 -> p $ >
  $ G -> a = suc (a - 1) -> p $ >
  $ G -> p $;

Step	Hyp	Ref	Expression
1		hyp h0	G -> a = 0 -> p
2		sub1can	a != 0 -> suc (a - 1) = a
3	2	conv ne	~a = 0 -> suc (a - 1) = a
4	3	eqcomd	~a = 0 -> a = suc (a - 1)
5		hyp h1	G -> a = suc (a - 1) -> p
6	4, 5	syl5	G -> ~a = 0 -> p
7	1, 6	casesd	G -> p

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, add0, addS)