Theorem lmemsS ≪ | index | src | ≫ 

pub theorem lmemsS (a l: nat): $ lmems (a : l) = a ; lmems l $;
StepHypRefExpression
1 eqtr 
lmems (a : l) = (\\ x, \\ z, \ y, x ; y) @ (a, l, lrec 0 (\\ x, \\ z, \ y, x ; y) l) ->
  (\\ x, \\ z, \ y, x ; y) @ (a, l, lrec 0 (\\ x, \\ z, \ y, x ; y) l) = a ; lmems l ->
  lmems (a : l) = a ; lmems l
2 lrecS 
lrec 0 (\\ x, \\ z, \ y, x ; y) (a : l) = (\\ x, \\ z, \ y, x ; y) @ (a, l, lrec 0 (\\ x, \\ z, \ y, x ; y) l)
3 2 conv lmems 
lmems (a : l) = (\\ x, \\ z, \ y, x ; y) @ (a, l, lrec 0 (\\ x, \\ z, \ y, x ; y) l)
4 1, 3 ax_mp 
(\\ x, \\ z, \ y, x ; y) @ (a, l, lrec 0 (\\ x, \\ z, \ y, x ; y) l) = a ; lmems l -> lmems (a : l) = a ; lmems l
5 anll 
x = a /\ z = l /\ y = lmems l -> x = a
6 anr 
x = a /\ z = l /\ y = lmems l -> y = lmems l
7 5, 6 inseqd 
x = a /\ z = l /\ y = lmems l -> x ; y = a ; lmems l
8 7 applamed 
x = a /\ z = l -> (\ y, x ; y) @ lmems l = a ; lmems l
9 8 appslamed 
x = a -> (\\ z, \ y, x ; y) @ (l, lmems l) = a ; lmems l
10 9 appslame 
(\\ x, \\ z, \ y, x ; y) @ (a, l, lmems l) = a ; lmems l
11 10 conv lmems 
(\\ x, \\ z, \ y, x ; y) @ (a, l, lrec 0 (\\ x, \\ z, \ y, x ; y) l) = a ; lmems l
12 4, 11 ax_mp 
lmems (a : l) = a ; lmems l

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 (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)