qed-.
theorem drops_conf_div: ∀f1,L,K. ⬇*[Ⓣ,f1] L ≘ K → ∀f2. ⬇*[Ⓣ,f2] L ≘ K →
- ð\9d\90\94â¦\83f1â¦\84 â\86\92 ð\9d\90\94â¦\83f2â¦\84 â\86\92 f1 â\89\97 f2.
+ ð\9d\90\94â¦\83f1â¦\84 â\86\92 ð\9d\90\94â¦\83f2â¦\84 â\86\92 f1 â\89¡ f2.
#f1 #L #K #H elim H -f1 -L -K
[ #f1 #Hf1 #f2 #Hf2 elim (drops_inv_atom1 … Hf2) -Hf2
/3 width=1 by isid_inv_eq_repl/
(* Basic_2A1: includes: drop_conf_lt *)
lemma drops_conf_skip1: ∀b2,f,L,L2. ⬇*[b2, f] L ≘ L2 →
∀b1,f1,I1,K1. ⬇*[b1, f1] L ≘ K1.ⓘ{I1} →
- â\88\80f2. f1 â\8a\9a â\86\91f2 ≘ f →
+ â\88\80f2. f1 â\8a\9a ⫯f2 ≘ f →
∃∃I2,K2. L2 = K2.ⓘ{I2} &
⬇*[b2, f2] K1 ≘ K2 & ⬆*[f2] I2 ≘ I1.
#b2 #f #L #L2 #H2 #b1 #f1 #I1 #K1 #H1 #f2 #Hf lapply (drops_conf … H1 … H2 … Hf) -L -Hf
(* Basic_2A1: includes: drop_trans_lt *)
lemma drops_trans_skip2: ∀b1,f1,L1,L. ⬇*[b1, f1] L1 ≘ L →
∀b2,f2,I2,K2. ⬇*[b2, f2] L ≘ K2.ⓘ{I2} →
- â\88\80f. f1 â\8a\9a f2 â\89\98 â\86\91f →
+ â\88\80f. f1 â\8a\9a f2 â\89\98 ⫯f →
∃∃I1,K1. L1 = K1.ⓘ{I1} &
⬇*[b1∧b2, f] K1 ≘ K2 & ⬆*[f] I2 ≘ I1.
#b1 #f1 #L1 #L #H1 #b2 #f2 #I2 #K2 #H2 #f #Hf
(* Basic_2A1: includes: drops_conf_div *)
lemma drops_conf_div_bind: ∀f1,f2,I1,I2,L,K.
⬇*[Ⓣ, f1] L ≘ K.ⓘ{I1} → ⬇*[Ⓣ, f2] L ≘ K.ⓘ{I2} →
- ð\9d\90\94â¦\83f1â¦\84 â\86\92 ð\9d\90\94â¦\83f2â¦\84 â\86\92 f1 â\89\97 f2 ∧ I1 = I2.
+ ð\9d\90\94â¦\83f1â¦\84 â\86\92 ð\9d\90\94â¦\83f2â¦\84 â\86\92 f1 â\89¡ f2 ∧ I1 = I2.
#f1 #f2 #I1 #I2 #L #K #Hf1 #Hf2 #HU1 #HU2
lapply (drops_isuni_fwd_drop2 … Hf1) // #H1
lapply (drops_isuni_fwd_drop2 … Hf2) // #H2