X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Frelocation%2Ffr2_minus.ma;h=d083a5df87e3f873ba62f75b3d5f058a60857dc9;hb=12dc655b7f5321b33b93a310d53e23e60e090caa;hp=edc241fc0b9f87f38c18ea1eef0df6300cd536c4;hpb=dd41efaab7f147d5673cc30a27d36375f9b52c9d;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/fr2_minus.ma b/matita/matita/contribs/lambdadelta/ground/relocation/fr2_minus.ma index edc241fc0..d083a5df8 100644 --- a/matita/matita/contribs/lambdadelta/ground/relocation/fr2_minus.ma +++ b/matita/matita/contribs/lambdadelta/ground/relocation/fr2_minus.ma @@ -24,8 +24,8 @@ include "ground/relocation/fr2_map.ma". (*** minuss *) inductive fr2_minus: nat → relation fr2_map ≝ (*** minuss_nil *) -| fr2_minus_nil (i): - fr2_minus i (◊) (◊) +| fr2_minus_empty (i): + fr2_minus i (𝐞) (𝐞) (*** minuss_lt *) | fr2_minus_lt (f1) (f2) (d) (h) (i): i < d → fr2_minus i f1 f2 → fr2_minus i (❨d,h❩;f1) (❨d-i,h❩;f2) @@ -41,9 +41,9 @@ interpretation (* Basic inversions *********************************************************) (*** minuss_inv_nil1 *) -lemma fr2_minus_inv_nil_sn (f2) (i): - ◊ ▭ i ≘ f2 → f2 = ◊. -#f2 #i @(insert_eq_1 … (◊)) +lemma fr2_minus_inv_empty_sn (f2) (i): + 𝐞 ▭ i ≘ f2 → f2 = 𝐞. +#f2 #i @(insert_eq_1 … (𝐞)) #f1 * -f1 -f2 -i [ // | #f1 #f2 #d #h #i #_ #_ #H destruct @@ -52,7 +52,7 @@ lemma fr2_minus_inv_nil_sn (f2) (i): qed-. (*** minuss_inv_cons1 *) -lemma fr2_minus_inv_cons_sn (f1) (f2) (d) (h) (i): +lemma fr2_minus_inv_lcons_sn (f1) (f2) (d) (h) (i): ❨d, h❩;f1 ▭ i ≘ f2 → ∨∨ ∧∧ d ≤ i & f1 ▭ h+i ≘ f2 | ∃∃f. i < d & f1 ▭ i ≘ f & f2 = ❨d-i,h❩;f. @@ -65,18 +65,18 @@ lemma fr2_minus_inv_cons_sn (f1) (f2) (d) (h) (i): qed-. (*** minuss_inv_cons1_ge *) -lemma fr2_minus_inv_cons_sn_ge (f1) (f2) (d) (h) (i): +lemma fr2_minus_inv_lcons_sn_ge (f1) (f2) (d) (h) (i): ❨d, h❩;f1 ▭ i ≘ f2 → d ≤ i → f1 ▭ h+i ≘ f2. #f1 #f2 #d #h #i #H -elim (fr2_minus_inv_cons_sn … H) -H * // #f #Hid #_ #_ #Hdi +elim (fr2_minus_inv_lcons_sn … H) -H * // #f #Hid #_ #_ #Hdi elim (nlt_ge_false … Hid Hdi) qed-. (*** minuss_inv_cons1_lt *) -lemma fr2_minus_inv_cons_sn_lt (f1) (f2) (d) (h) (i): +lemma fr2_minus_inv_lcons_sn_lt (f1) (f2) (d) (h) (i): ❨d, h❩;f1 ▭ i ≘ f2 → i < d → ∃∃f. f1 ▭ i ≘ f & f2 = ❨d-i,h❩;f. -#f1 #f2 #d #h #i #H elim (fr2_minus_inv_cons_sn … H) -H * +#f1 #f2 #d #h #i #H elim (fr2_minus_inv_lcons_sn … H) -H * [ #Hdi #_ #Hid elim (nlt_ge_false … Hid Hdi) | /2 width=3 by ex2_intro/ ]