Theorem Arrayeqd | index | src |

theorem Arrayeqd (_G: wff) (_A1 _A2: set) (_n1 _n2: nat):
  $ _G -> _A1 == _A2 $ >
  $ _G -> _n1 = _n2 $ >
  $ _G -> Array _A1 _n1 == Array _A2 _n2 $;
StepHypRefExpression
1 eqidd
_G -> l = l
2 hyp _Ah
_G -> _A1 == _A2
3 2 Listeqd
_G -> List _A1 == List _A2
4 1, 3 eleqd
_G -> (l e. List _A1 <-> l e. List _A2)
5 eqidd
_G -> len l = len l
6 hyp _nh
_G -> _n1 = _n2
7 5, 6 eqeqd
_G -> (len l = _n1 <-> len l = _n2)
8 4, 7 aneqd
_G -> (l e. List _A1 /\ len l = _n1 <-> l e. List _A2 /\ len l = _n2)
9 8 abeqd
_G -> {l | l e. List _A1 /\ len l = _n1} == {l | l e. List _A2 /\ len l = _n2}
10 9 conv Array
_G -> Array _A1 _n1 == Array _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)