Theorem repeateqd | index | src |

theorem repeateqd (_G: wff) (_a1 _a2 _n1 _n2: nat):
  $ _G -> _a1 = _a2 $ >
  $ _G -> _n1 = _n2 $ >
  $ _G -> repeat _a1 _n1 = repeat _a2 _n2 $;
StepHypRefExpression
1 eqidd
_G -> 0 = 0
2 hyp _ah
_G -> _a1 = _a2
3 eqidd
_G -> x = x
4 2, 3 conseqd
_G -> _a1 : x = _a2 : x
5 4 lameqd
_G -> \ x, _a1 : x == \ x, _a2 : x
6 hyp _nh
_G -> _n1 = _n2
7 1, 5, 6 receqd
_G -> rec 0 (\ x, _a1 : x) _n1 = rec 0 (\ x, _a2 : x) _n2
8 7 conv repeat
_G -> repeat _a1 _n1 = repeat _a2 _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)