include "nat/plus.ma".
-ntheorem foo: \forall x, y. ((λz. x + x = z + z) ?).
-##[ #x; #y; nnormalize; nauto.
\ No newline at end of file
+(*ntheorem boo:
+ (∀x. x = x) → 0 = 0.
+##[ #H; nwhd in H ⊢ %; nauto by H.*)
+
+ntheorem bboo:
+ (∀x. x + 0 = x) ->
+ (∀x, y. x + S y = S (x + y)) →
+ (∀x, y. x + y = y + x) →
+ 3 + 2 = 5.
+#H; #H1; #H2; nauto by H, H1. H2.
+
+ntheorem foo:
+ ((λx.x + 0 = x) ?) →
+ ((λx,y.x + S y = S (x + y)) ? ?) →
+ ((λx,y.x y = x y) ? ?) →
+ ∀x. ((λz. x + x = z + z) ?).
+##[ #H; #H1; #H2; #x; nwhd in H H1 H2 ⊢ %; nauto by H, H1, H2.
\ No newline at end of file