Theorem appendS ≪ | index | src | ≫ 

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

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)