Theorem splitb | index | src |

theorem splitb (G: wff) (a: nat) (p: wff):
  $ G -> a = b0 (a // 2) -> p $ >
  $ G -> a = b1 (a // 2) -> p $ >
  $ G -> p $;
StepHypRefExpression
1 b0orb1
a = b0 (a // 2) \/ a = b1 (a // 2)
2 hyp h0
G -> a = b0 (a // 2) -> p
3 hyp h1
G -> a = b1 (a // 2) -> p
4 2, 3 eord
G -> a = b0 (a // 2) \/ a = b1 (a // 2) -> p
5 1, 4 mpi
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, muleq, add0, addS, mul0, mulS)