Theorem ocaseeq | index | src |

theorem ocaseeq (_z1 _z2: nat) (_S1 _S2: set):
  $ _z1 = _z2 -> _S1 == _S2 -> ocase _z1 _S1 == ocase _z2 _S2 $;
StepHypRefExpression
1 anl
_z1 = _z2 /\ _S1 == _S2 -> _z1 = _z2
2 anr
_z1 = _z2 /\ _S1 == _S2 -> _S1 == _S2
3 1, 2 ocaseeqd
_z1 = _z2 /\ _S1 == _S2 -> ocase _z1 _S1 == ocase _z2 _S2
4 3 exp
_z1 = _z2 -> _S1 == _S2 -> ocase _z1 _S1 == ocase _z2 _S2

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 (peano2, addeq, muleq)