some restyling ...

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / relocation / drops_length.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_length.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_length.ma
index 94085a331cce0eb0792cfcbbc2e749106e03a5e4..1a20d722f2e8160f4a20e89515bcd261b91da5fb 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_length.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_length.ma
@@ -20,13 +20,13 @@ include "static_2/relocation/drops.ma".
 (* Forward lemmas with length for local environments ************************)
 
 (* Basic_2A1: includes: drop_fwd_length_le4 *)
-lemma drops_fwd_length_le4: ∀b,f,L1,L2. ⬇*[b, f] L1 ≘ L2 → |L2| ≤ |L1|.
+lemma drops_fwd_length_le4: ∀b,f,L1,L2. ⬇*[b,f] L1 ≘ L2 → |L2| ≤ |L1|.
 #b #f #L1 #L2 #H elim H -f -L1 -L2 /2 width=1 by le_S, le_S_S/
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_eq1 *)
-theorem drops_fwd_length_eq1: ∀b1,b2,f,L1,K1. ⬇*[b1, f] L1 ≘ K1 →
-                              ∀L2,K2. ⬇*[b2, f] L2 ≘ K2 →
+theorem drops_fwd_length_eq1: ∀b1,b2,f,L1,K1. ⬇*[b1,f] L1 ≘ K1 →
+                              ∀L2,K2. ⬇*[b2,f] L2 ≘ K2 →
                               |L1| = |L2| → |K1| = |K2|.
 #b1 #b2 #f #L1 #K1 #HLK1 elim HLK1 -f -L1 -K1
 [ #f #_ #L2 #K2 #HLK2 #H lapply (length_inv_zero_sn … H) -H
@@ -43,7 +43,7 @@ qed-.
 
 (* forward lemmas with finite colength assignment ***************************)
 
-lemma drops_fwd_fcla: ∀f,L1,L2. ⬇*[Ⓣ, f] L1 ≘ L2 →
+lemma drops_fwd_fcla: ∀f,L1,L2. ⬇*[Ⓣ,f] L1 ≘ L2 →
                       ∃∃n. 𝐂⦃f⦄ ≘ n & |L1| = |L2| + n.
 #f #L1 #L2 #H elim H -f -L1 -L2
 [ /4 width=3 by fcla_isid, ex2_intro/
@@ -53,25 +53,25 @@ lemma drops_fwd_fcla: ∀f,L1,L2. ⬇*[Ⓣ, f] L1 ≘ L2 →
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length *)
-lemma drops_fcla_fwd: ∀f,L1,L2,n. ⬇*[Ⓣ, f] L1 ≘ L2 → 𝐂⦃f⦄ ≘ n →
+lemma drops_fcla_fwd: ∀f,L1,L2,n. ⬇*[Ⓣ,f] L1 ≘ L2 → 𝐂⦃f⦄ ≘ n →
                       |L1| = |L2| + n.
 #f #l1 #l2 #n #Hf #Hn elim (drops_fwd_fcla … Hf) -Hf
 #k #Hm #H <(fcla_mono … Hm … Hn) -f //
 qed-.
 
-lemma drops_fwd_fcla_le2: ∀f,L1,L2. ⬇*[Ⓣ, f] L1 ≘ L2 →
+lemma drops_fwd_fcla_le2: ∀f,L1,L2. ⬇*[Ⓣ,f] L1 ≘ L2 →
                           ∃∃n. 𝐂⦃f⦄ ≘ n & n ≤ |L1|.
 #f #L1 #L2 #H elim (drops_fwd_fcla … H) -H /2 width=3 by ex2_intro/
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_le2 *)
-lemma drops_fcla_fwd_le2: ∀f,L1,L2,n. ⬇*[Ⓣ, f] L1 ≘ L2 → 𝐂⦃f⦄ ≘ n →
+lemma drops_fcla_fwd_le2: ∀f,L1,L2,n. ⬇*[Ⓣ,f] L1 ≘ L2 → 𝐂⦃f⦄ ≘ n →
                           n ≤ |L1|.
 #f #L1 #L2 #n #H #Hn elim (drops_fwd_fcla_le2 … H) -H
 #k #Hm #H <(fcla_mono … Hm … Hn) -f //
 qed-.
 
-lemma drops_fwd_fcla_lt2: ∀f,L1,I2,K2. ⬇*[Ⓣ, f] L1 ≘ K2.ⓘ{I2} →
+lemma drops_fwd_fcla_lt2: ∀f,L1,I2,K2. ⬇*[Ⓣ,f] L1 ≘ K2.ⓘ{I2} →
                           ∃∃n. 𝐂⦃f⦄ ≘ n & n < |L1|.
 #f #L1 #I2 #K2 #H elim (drops_fwd_fcla … H) -H
 #n #Hf #H >H -L1 /3 width=3 by le_S_S, ex2_intro/
@@ -79,27 +79,27 @@ qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_lt2 *)
 lemma drops_fcla_fwd_lt2: ∀f,L1,I2,K2,n.
-                          ⬇*[Ⓣ, f] L1 ≘ K2.ⓘ{I2} → 𝐂⦃f⦄ ≘ n →
+                          ⬇*[Ⓣ,f] L1 ≘ K2.ⓘ{I2} → 𝐂⦃f⦄ ≘ n →
                           n < |L1|.
 #f #L1 #I2 #K2 #n #H #Hn elim (drops_fwd_fcla_lt2 … H) -H
 #k #Hm #H <(fcla_mono … Hm … Hn) -f //
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_lt4 *)
-lemma drops_fcla_fwd_lt4: ∀f,L1,L2,n. ⬇*[Ⓣ, f] L1 ≘ L2 → 𝐂⦃f⦄ ≘ n → 0 < n →
+lemma drops_fcla_fwd_lt4: ∀f,L1,L2,n. ⬇*[Ⓣ,f] L1 ≘ L2 → 𝐂⦃f⦄ ≘ n → 0 < n →
                           |L2| < |L1|.
 #f #L1 #L2 #n #H #Hf #Hn lapply (drops_fcla_fwd … H Hf) -f
 /2 width=1 by lt_minus_to_plus_r/ qed-.
 
 (* Basic_2A1: includes: drop_inv_length_eq *)
-lemma drops_inv_length_eq: ∀f,L1,L2. ⬇*[Ⓣ, f] L1 ≘ L2 → |L1| = |L2| → 𝐈⦃f⦄.
+lemma drops_inv_length_eq: ∀f,L1,L2. ⬇*[Ⓣ,f] L1 ≘ L2 → |L1| = |L2| → 𝐈⦃f⦄.
 #f #L1 #L2 #H #HL12 elim (drops_fwd_fcla … H) -H
 #n #Hn <HL12 -L2 #H lapply (discr_plus_x_xy … H) -H
 /2 width=3 by fcla_inv_xp/
 qed-.
 
 (* Basic_2A1: includes: drop_fwd_length_eq2 *)
-theorem drops_fwd_length_eq2: ∀f,L1,L2,K1,K2. ⬇*[Ⓣ, f] L1 ≘ K1 → ⬇*[Ⓣ, f] L2 ≘ K2 →
+theorem drops_fwd_length_eq2: ∀f,L1,L2,K1,K2. ⬇*[Ⓣ,f] L1 ≘ K1 → ⬇*[Ⓣ,f] L2 ≘ K2 →
                               |K1| = |K2| → |L1| = |L2|.
 #f #L1 #L2 #K1 #K2 #HLK1 #HLK2 #HL12
 elim (drops_fwd_fcla … HLK1) -HLK1 #n1 #Hn1 #H1 >H1 -L1
@@ -107,7 +107,7 @@ elim (drops_fwd_fcla … HLK2) -HLK2 #n2 #Hn2 #H2 >H2 -L2
 <(fcla_mono … Hn2 … Hn1) -f //
 qed-.
 
-theorem drops_conf_div: ∀f1,f2,L1,L2. ⬇*[Ⓣ, f1] L1 ≘ L2 → ⬇*[Ⓣ, f2] L1 ≘ L2 →
+theorem drops_conf_div: ∀f1,f2,L1,L2. ⬇*[Ⓣ,f1] L1 ≘ L2 → ⬇*[Ⓣ,f2] L1 ≘ L2 →
                         ∃∃n. 𝐂⦃f1⦄ ≘ n & 𝐂⦃f2⦄ ≘ n.
 #f1 #f2 #L1 #L2 #H1 #H2
 elim (drops_fwd_fcla … H1) -H1 #n1 #Hf1 #H1
@@ -116,7 +116,7 @@ lapply (injective_plus_r … H) -L2 #H destruct /2 width=3 by ex2_intro/
 qed-.
 
 theorem drops_conf_div_fcla: ∀f1,f2,L1,L2,n1,n2.
-                             ⬇*[Ⓣ, f1] L1 ≘ L2 → ⬇*[Ⓣ, f2] L1 ≘ L2 → 𝐂⦃f1⦄ ≘ n1 → 𝐂⦃f2⦄ ≘ n2 →
+                             ⬇*[Ⓣ,f1] L1 ≘ L2 → ⬇*[Ⓣ,f2] L1 ≘ L2 → 𝐂⦃f1⦄ ≘ n1 → 𝐂⦃f2⦄ ≘ n2 →
                              n1 = n2.
 #f1 #f2 #L1 #L2 #n1 #n2 #Hf1 #Hf2 #Hn1 #Hn2
 lapply (drops_fcla_fwd … Hf1 Hn1) -f1 #H1