(* *)
(**************************************************************************)
+include "ground_2/xoa/and_4.ma".
+include "ground_2/xoa/ex_4_2.ma".
+include "ground_2/xoa/or_4.ma".
include "static_2/notation/relations/supterm_6.ma".
include "static_2/notation/relations/supterm_7.ma".
include "static_2/syntax/lenv.ma".
| fqu_bind_dx: ∀p,I,G,L,V,T. b = Ⓣ → fqu b G L (ⓑ{p,I}V.T) G (L.ⓑ{I}V) T
| fqu_clear : ∀p,I,G,L,V,T. b = Ⓕ → fqu b G L (ⓑ{p,I}V.T) G (L.ⓧ) T
| fqu_flat_dx: ∀I,G,L,V,T. fqu b G L (ⓕ{I}V.T) G L T
-| fqu_drop : â\88\80I,G,L,T,U. â¬\86*[1] T ≘ U → fqu b G (L.ⓘ{I}) U G L T
+| fqu_drop : â\88\80I,G,L,T,U. â\87§*[1] T ≘ U → fqu b G (L.ⓘ{I}) U G L T
.
interpretation
∨∨ ∧∧ G1 = G2 & L1 = L2 & V1 = T2
| ∧∧ G1 = G2 & L1.ⓑ{I}V1 = L2 & U1 = T2 & b = Ⓣ
| ∧∧ G1 = G2 & L1.ⓧ = L2 & U1 = T2 & b = Ⓕ
- | â\88\83â\88\83J. G1 = G2 & L1 = L2.â\93\98{J} & â¬\86*[1] T2 ≘ ⓑ{p,I}V1.U1.
+ | â\88\83â\88\83J. G1 = G2 & L1 = L2.â\93\98{J} & â\87§*[1] T2 ≘ ⓑ{p,I}V1.U1.
#b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
[ #I #G #L #T #q #J #V0 #U0 #H destruct
| #I #G #L #V #T #q #J #V0 #U0 #H destruct /3 width=1 by and3_intro, or4_intro0/
∨∨ ∧∧ G1 = G2 & L1 = L2 & V1 = T2
| ∧∧ G1 = G2 & L1.ⓑ{I}V1 = L2 & U1 = T2 & b = Ⓣ
| ∧∧ G1 = G2 & L1.ⓧ = L2 & U1 = T2 & b = Ⓕ
- | â\88\83â\88\83J. G1 = G2 & L1 = L2.â\93\98{J} & â¬\86*[1] T2 ≘ ⓑ{p,I}V1.U1.
+ | â\88\83â\88\83J. G1 = G2 & L1 = L2.â\93\98{J} & â\87§*[1] T2 ≘ ⓑ{p,I}V1.U1.
/2 width=4 by fqu_inv_bind1_aux/ qed-.
lemma fqu_inv_bind1_true: ∀p,I,G1,G2,L1,L2,V1,U1,T2. ⦃G1,L1,ⓑ{p,I}V1.U1⦄ ⬂ ⦃G2,L2,T2⦄ →
∨∨ ∧∧ G1 = G2 & L1 = L2 & V1 = T2
| ∧∧ G1 = G2 & L1.ⓑ{I}V1 = L2 & U1 = T2
- | â\88\83â\88\83J. G1 = G2 & L1 = L2.â\93\98{J} & â¬\86*[1] T2 ≘ ⓑ{p,I}V1.U1.
+ | â\88\83â\88\83J. G1 = G2 & L1 = L2.â\93\98{J} & â\87§*[1] T2 ≘ ⓑ{p,I}V1.U1.
#p #I #G1 #G2 #L1 #L2 #V1 #U1 #T2 #H elim (fqu_inv_bind1 … H) -H
/3 width=1 by or3_intro0, or3_intro2/
* #HG #HL #HU #H destruct
∀I,V1,U1. T1 = ⓕ{I}V1.U1 →
∨∨ ∧∧ G1 = G2 & L1 = L2 & V1 = T2
| ∧∧ G1 = G2 & L1 = L2 & U1 = T2
- | â\88\83â\88\83J. G1 = G2 & L1 = L2.â\93\98{J} & â¬\86*[1] T2 ≘ ⓕ{I}V1.U1.
+ | â\88\83â\88\83J. G1 = G2 & L1 = L2.â\93\98{J} & â\87§*[1] T2 ≘ ⓕ{I}V1.U1.
#b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
[ #I #G #L #T #J #V0 #U0 #H destruct
| #I #G #L #V #T #J #V0 #U0 #H destruct /3 width=1 by and3_intro, or3_intro0/
lemma fqu_inv_flat1: ∀b,I,G1,G2,L1,L2,V1,U1,T2. ⦃G1,L1,ⓕ{I}V1.U1⦄ ⬂[b] ⦃G2,L2,T2⦄ →
∨∨ ∧∧ G1 = G2 & L1 = L2 & V1 = T2
| ∧∧ G1 = G2 & L1 = L2 & U1 = T2
- | â\88\83â\88\83J. G1 = G2 & L1 = L2.â\93\98{J} & â¬\86*[1] T2 ≘ ⓕ{I}V1.U1.
+ | â\88\83â\88\83J. G1 = G2 & L1 = L2.â\93\98{J} & â\87§*[1] T2 ≘ ⓕ{I}V1.U1.
/2 width=4 by fqu_inv_flat1_aux/ qed-.
(* Advanced inversion lemmas ************************************************)