Theorem sreceq | index | src |

theorem sreceq (_S1 _S2: set) (_n1 _n2: nat):
  $ _S1 == _S2 -> _n1 = _n2 -> srec _S1 _n1 = srec _S2 _n2 $;
StepHypRefExpression
1 anl
_S1 == _S2 /\ _n1 = _n2 -> _S1 == _S2
2 anr
_S1 == _S2 /\ _n1 = _n2 -> _n1 = _n2
3 1, 2 sreceqd
_S1 == _S2 /\ _n1 = _n2 -> srec _S1 _n1 = srec _S2 _n2
4 3 exp
_S1 == _S2 -> _n1 = _n2 -> srec _S1 _n1 = srec _S2 _n2

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)