Theorem mapeqd ≪ | index | src | ≫ 

theorem mapeqd (_G: wff) (_F1 _F2: set) (_l1 _l2: nat):
  $ _G -> _F1 == _F2 $ >
  $ _G -> _l1 = _l2 $ >
  $ _G -> map _F1 _l1 = map _F2 _l2 $;
StepHypRefExpression
1 eqidd 
_G -> 0 = 0
2 hyp _Fh 
_G -> _F1 == _F2
3 eqidd 
_G -> a = a
4 2, 3 appeqd 
_G -> _F1 @ a = _F2 @ a
5 eqidd 
_G -> ih = ih
6 4, 5 conseqd 
_G -> _F1 @ a : ih = _F2 @ a : ih
7 6 lameqd 
_G -> \ ih, _F1 @ a : ih == \ ih, _F2 @ a : ih
8 7 slameqd 
_G -> (\\ z, \ ih, _F1 @ a : ih) == (\\ z, \ ih, _F2 @ a : ih)
9 8 slameqd 
_G -> (\\ a, \\ z, \ ih, _F1 @ a : ih) == (\\ a, \\ z, \ ih, _F2 @ a : ih)
10 hyp _lh 
_G -> _l1 = _l2
11 1, 9, 10 lreceqd 
_G -> lrec 0 (\\ a, \\ z, \ ih, _F1 @ a : ih) _l1 = lrec 0 (\\ a, \\ z, \ ih, _F2 @ a : ih) _l2
12 11 conv map 
_G -> map _F1 _l1 = map _F2 _l2

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)