(* Basic_2A1: includes: lreq_drop_trans_be *)
lemma lreq_drops_trans_next: ∀f2,L1,L2. L1 ≡[f2] L2 →
∀b,f,I,K2. ⬇*[b, f] L2 ≘ K2.ⓘ{I} → 𝐔⦃f⦄ →
- â\88\80f1. f ~â\8a\9a ⫯f1 ≘ f2 →
+ â\88\80f1. f ~â\8a\9a â\86\91f1 ≘ f2 →
∃∃K1. ⬇*[b, f] L1 ≘ K1.ⓘ{I} & K1 ≡[f1] K2.
#f2 #L1 #L2 #HL12 #b #f #I2 #K2 #HLK2 #Hf #f1 #Hf2
elim (lexs_drops_trans_next … HL12 … HLK2 Hf … Hf2) -f2 -L2 -Hf
(* Basic_2A1: includes: lreq_drop_conf_be *)
lemma lreq_drops_conf_next: ∀f2,L1,L2. L1 ≡[f2] L2 →
∀b,f,I,K1. ⬇*[b, f] L1 ≘ K1.ⓘ{I} → 𝐔⦃f⦄ →
- â\88\80f1. f ~â\8a\9a ⫯f1 ≘ f2 →
+ â\88\80f1. f ~â\8a\9a â\86\91f1 ≘ f2 →
∃∃K2. ⬇*[b, f] L2 ≘ K2.ⓘ{I} & K1 ≡[f1] K2.
#f2 #L1 #L2 #HL12 #b #f #I1 #K1 #HLK1 #Hf #f1 #Hf2
elim (lreq_drops_trans_next … (lreq_sym … HL12) … HLK1 … Hf2) // -f2 -L1 -Hf
lemma drops_lreq_trans_next: ∀f1,K1,K2. K1 ≡[f1] K2 →
∀b,f,I,L1. ⬇*[b, f] L1.ⓘ{I} ≘ K1 →
- â\88\80f2. f ~â\8a\9a f1 â\89\98 ⫯f2 →
+ â\88\80f2. f ~â\8a\9a f1 â\89\98 â\86\91f2 →
∃∃L2. ⬇*[b, f] L2.ⓘ{I} ≘ K2 & L1 ≡[f2] L2 & L1.ⓘ{I} ≡[f] L2.ⓘ{I}.
#f1 #K1 #K2 #HK12 #b #f #I1 #L1 #HLK1 #f2 #Hf2
elim (drops_lexs_trans_next … HK12 … HLK1 … Hf2) -f1 -K1