- [ lapply add_gen_O_2 to H as H0. clear H.
- rewrite > H0 in H1. clear H0. clear p
- | lapply add_gen_S_2 to H1 as H0. clear H1.
- decompose H0.
- rewrite > H3. clear H3. clear r1.
- lapply add_gen_S_2 to H2 as H0. clear H2.
- decompose H0.
- rewrite > H2. clear H2. clear r2.
- ]; auto.
-qed.
-
-
-
-theorem add_gen_eq_2_3: \forall p,q. add p q q \to p = O.
- intros 2. elim q; clear q; intros;
- [ lapply add_gen_O_2 to H as H0. clear H.
- rewrite > H0. clear H0. clear p
- | lapply add_gen_S_2 to H1 as H0. clear H1.
- decompose H0.
- lapply eq_gen_S_S to H2 as H0. clear H2.
- rewrite < H0 in H3. clear H0. clear a
+ [ lapply linear add_gen_O_2 to H as H0.
+ rewrite > H0 in H1. clear H0 p
+ | lapply linear add_gen_S_2 to H1 as H0.
+ decompose.
+ rewrite > H3. clear H3 r1.
+ lapply linear add_gen_S_2 to H2 as H0.
+ decompose.
+ rewrite > H2. clear H2 r2.