include "Lift/fwd.ma".
-alias id "nplus_conf" = "cic:/matita/RELATIONAL/NPlus/props/nplus_conf.con".
-
-axiom pippo: \forall x,y. x < y \to y <= x \to False.
-
-theorem lift_conf: \forall q,h,d,t,x. Lift q h d t x \to
- \forall y. Lift q h d t y \to
+theorem lift_conf: \forall l,i,t,x. Lift l i t x \to
+ \forall y. Lift l i t y \to
x = y.
- intros 6. elim H; clear H q h d t x;
- [ lapply linear lift_sort_fwd to H1.
+ intros 5. elim H; clear H i t x;
+ [ lapply linear lift_inv_sort_1 to H1.
subst. auto
- | lapply linear lift_lref_fwd to H1.
- decompose; subst;
- [ auto | destruct H1 | destruct H ]
- | lapply linear lift_lref_fwd to H2.
+ | lapply linear lift_inv_lref_1 to H2.
decompose; subst;
- [ destruct H | auto | lapply pippo to H1, H4. decompose ]
- | lapply linear lift_lref_fwd to H3.
+ [ auto | lapply nle_false to H2, H1. decompose ]
+ | lapply linear lift_inv_lref_1 to H3.
decompose; subst;
- [ destruct H
- | lapply linear pippo to H5, H1. decompose
- | lapply linear nplus_conf to H2, H4. subst. auto
+ [ lapply linear nle_false to H1, H3. decompose
+ | lapply linear nplus_conf to H2, H4. subst. auto
]
+ | lapply linear lift_inv_bind_1 to H5.
+ decompose. subst. auto.
+ | lapply linear lift_inv_flat_1 to H5.
+ decompose. subst. auto.
+ ].
+qed.
+
+alias id "nle_trans" = "cic:/matita/RELATIONAL/NLE/props/nle_trans.con".
+alias id "pippo" = "cic:/matita/RELATIONAL/NLE/nplus/pippo.con".
+alias id "nle_refl" = "cic:/matita/RELATIONAL/NLE/props/nle_refl.con".
-(*
-theorem lift_ct_le: \forall q,h,d,t,y. (Lift q h d t y) \to
- \forall k,e,x. (Lift q k e t x) \to
- \forall z. (Lift q k e y z) \to
- e <= d \to \forall d'. (k + d == d') \to
- (Lift q h d' x z).
- intros 6. elim H; clear H q h d t y;
- [ lapply linear lift_sort_fwd to H1.
- lapply linear lift_sort_fwd to H2.
+theorem lift_ct_le: \forall l1,i1,t,y. (Lift l1 i1 t y) \to
+ \forall l2,i2,x. (Lift l2 i2 t x) \to
+ \forall z. (Lift l2 i2 y z) \to
+ i2 <= i1 \to \forall i. (l2 + i1 == i) \to
+ (Lift l1 i x z).
+ intros 5. elim H; clear H i1 t y;
+ [ lapply lift_conf to H1, H2. clear H2. subst.
+ lapply linear lift_inv_sort_1 to H1.
subst. auto
- | lapply linear lift_lref_fwd to H1.
- lapply linear lift_lref_fwd to H2.
- decompose; subst;
- [ auto
- | auto
- |
- *)
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+ | lapply lift_conf to H2, H3. clear H3. subst.
+ lapply linear lift_inv_lref_1 to H2.
+ decompose; subst; clear H2 H4 i2;
+ [ lapply linear nle_nplus to H5 as H. clear l2. (**)
+ lapply linear nle_trans to H1, H.
+ auto
+ | lapply pippo to H3, H5; [ auto | apply nle_refl | auto ]. (**)
+ ]
+ |
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