(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/RELATIONAL/NPlus/fun".
+
include "NPlus/inv.ma".
theorem nplus_total: \forall p,q. \exists r. p + q == r.
intros 2. elim q; clear q;
- [ auto | decompose. auto ].
+ [ autobatch | decompose. autobatch ].
qed.
theorem nplus_mono: \forall p,q,r1. (p + q == r1) \to
\forall r2. (p + q == r2) \to r1 = r2.
intros 4. elim H; clear H q r1;
- [ lapply linear nplus_gen_zero_2 to H1
- | lapply linear nplus_gen_succ_2 to H3. decompose
- ]; subst; auto.
+ [ lapply linear nplus_inv_zero_2 to H1
+ | lapply linear nplus_inv_succ_2 to H3. decompose
+ ]; destruct; autobatch.
qed.
theorem nplus_inj_1: \forall p1, q, r. (p1 + q == r) \to
\forall p2. (p2 + q == r) \to p2 = p1.
intros 4. elim H; clear H q r;
- [ lapply linear nplus_gen_zero_2 to H1
- | lapply linear nplus_gen_succ_2_3 to H3
- ]; auto.
+ [ lapply linear nplus_inv_zero_2 to H1
+ | lapply linear nplus_inv_succ_2_3 to H3
+ ]; autobatch.
qed.