/2 width=1 by lfxs_pair/ qed.
lemma lfpr_lref: ∀h,I1,I2,G,L1,L2,i.
- â¦\83G, L1â¦\84 â\8a¢ â\9e¡[h, #i] L2 â\86\92 â¦\83G, L1.â\93\98{I1}â¦\84 â\8a¢ â\9e¡[h, #⫯i] L2.ⓘ{I2}.
+ â¦\83G, L1â¦\84 â\8a¢ â\9e¡[h, #i] L2 â\86\92 â¦\83G, L1.â\93\98{I1}â¦\84 â\8a¢ â\9e¡[h, #â\86\91i] L2.ⓘ{I2}.
/2 width=1 by lfxs_lref/ qed.
lemma lfpr_gref: ∀h,I1,I2,G,L1,L2,l.
Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
/2 width=1 by lfxs_inv_zero/ qed-.
*)
-lemma lfpr_inv_lref: â\88\80h,G,Y1,Y2,i. â¦\83G, Y1â¦\84 â\8a¢ â\9e¡[h, #⫯i] Y2 →
+lemma lfpr_inv_lref: â\88\80h,G,Y1,Y2,i. â¦\83G, Y1â¦\84 â\8a¢ â\9e¡[h, #â\86\91i] Y2 →
∨∨ Y1 = ⋆ ∧ Y2 = ⋆
| ∃∃I1,I2,L1,L2. ⦃G, L1⦄ ⊢ ➡[h, #i] L2 &
Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}.
Y1 = L1.ⓑ{I}V1.
/2 width=1 by lfxs_inv_zero_pair_dx/ qed-.
-lemma lfpr_inv_lref_bind_sn: â\88\80h,I1,G,Y2,L1,i. â¦\83G, L1.â\93\98{I1}â¦\84 â\8a¢ â\9e¡[h, #⫯i] Y2 →
+lemma lfpr_inv_lref_bind_sn: â\88\80h,I1,G,Y2,L1,i. â¦\83G, L1.â\93\98{I1}â¦\84 â\8a¢ â\9e¡[h, #â\86\91i] Y2 →
∃∃I2,L2. ⦃G, L1⦄ ⊢ ➡[h, #i] L2 & Y2 = L2.ⓘ{I2}.
/2 width=2 by lfxs_inv_lref_bind_sn/ qed-.
-lemma lfpr_inv_lref_bind_dx: â\88\80h,I2,G,Y1,L2,i. â¦\83G, Y1â¦\84 â\8a¢ â\9e¡[h, #⫯i] L2.ⓘ{I2} →
+lemma lfpr_inv_lref_bind_dx: â\88\80h,I2,G,Y1,L2,i. â¦\83G, Y1â¦\84 â\8a¢ â\9e¡[h, #â\86\91i] L2.ⓘ{I2} →
∃∃I1,L1. ⦃G, L1⦄ ⊢ ➡[h, #i] L2 & Y1 = L1.ⓘ{I1}.
/2 width=2 by lfxs_inv_lref_bind_dx/ qed-.