partial commit in static_2

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_weight.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_weight.ma
index 975b01523d5fe71972abe1270b33e7188475292b..97b730cc82d8983ce20be9581b520f48ce5deb6b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_weight.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_weight.ma
@@ -23,9 +23,9 @@ include "static_2/relocation/drops.ma".
 (* Basic_2A1: includes: drop_fwd_lw *)
 lemma drops_fwd_lw: ∀b,f,L1,L2. ⇩*[b,f] L1 ≘ L2 → ♯❨L2❩ ≤ ♯❨L1❩.
 #b #f #L1 #L2 #H elim H -f -L1 -L2 //
-[ /2 width=3 by transitive_le/
+[ /2 width=3 by nle_trans/
 | #f #I1 #I2 #L1 #L2 #_ #HI21 #IHL12 normalize
-  >(liftsb_fwd_bw … HI21) -HI21 /2 width=1 by monotonic_le_plus_l/
+  >(liftsb_fwd_bw … HI21) -HI21 /2 width=1 by nle_plus_bi_dx/
 ]
 qed-.
 
@@ -34,9 +34,9 @@ lemma drops_fwd_lw_lt: ∀f,L1,L2. ⇩*[Ⓣ,f] L1 ≘ L2 →
                        (𝐈❪f❫ → ⊥) → ♯❨L2❩ < ♯❨L1❩.
 #f #L1 #L2 #H elim H -f -L1 -L2
 [ #f #Hf #Hnf elim Hnf -Hnf /2 width=1 by/
-| /3 width=3 by drops_fwd_lw, le_to_lt_to_lt/
+| /3 width=3 by drops_fwd_lw, nle_nlt_trans/
 | #f #I1 #I2 #L1 #L2 #_ #HI21 #IHL12 #H normalize in ⊢ (?%%);
-  >(liftsb_fwd_bw … HI21) -I2 /5 width=3 by isid_push, monotonic_lt_plus_l/
+  >(liftsb_fwd_bw … HI21) -I2 /5 width=3 by pr_isi_push, nlt_plus_bi_dx/
 ]
 qed-.
 
@@ -45,12 +45,12 @@ qed-.
 (* Basic_2A1: includes: drop_fwd_rfw *)
 lemma drops_bind2_fwd_rfw: ∀b,f,I,L,K,V. ⇩*[b,f] L ≘ K.ⓑ[I]V → ∀T. ♯❨K,V❩ < ♯❨L,T❩.
 #b #f #I #L #K #V #HLK lapply (drops_fwd_lw … HLK) -HLK
-normalize in ⊢ (%→?→?%%); /3 width=3 by le_to_lt_to_lt, monotonic_lt_plus_r/
+normalize in ⊢ (%→?→?%%); /3 width=3 by nle_nlt_trans, nlt_plus_bi_sn/
 qed-.
 
 (* Advanced inversion lemma *************************************************)
 
 lemma drops_inv_x_bind_xy: ∀b,f,I,L. ⇩*[b,f] L ≘ L.ⓘ[I] → ⊥.
 #b #f #I #L #H lapply (drops_fwd_lw … H) -b -f
-/2 width=4 by lt_le_false/ (**) (* full auto is a bit slow: 19s *)
+/2 width=4 by nlt_ge_false/ (**) (* full auto is a bit slow: 19s *)
 qed-.