-lemma cpg_inv_appl1: ∀Rt,c,h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓐV1.U1 ⬈[Rt, c, h] U2 →
- ∨∨ ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[Rt, cV, h] V2 & ⦃G, L⦄ ⊢ U1 ⬈[Rt, cT, h] T2 &
- U2 = â\93\90V2.T2 & c = ((â\86\93cV)∨cT)
- | ∃∃cV,cW,cT,p,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ⬈[Rt, cV, h] V2 & ⦃G, L⦄ ⊢ W1 ⬈[Rt, cW, h] W2 & ⦃G, L.ⓛW1⦄ ⊢ T1 ⬈[Rt, cT, h] T2 &
- U1 = â\93\9b{p}W1.T1 & U2 = â\93\93{p}â\93\9dW2.V2.T2 & c = ((â\86\93cV)â\88¨(â\86\93cW)∨cT)+𝟙𝟘
- | ∃∃cV,cW,cT,p,V,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ⬈[Rt, cV, h] V & ⬆*[1] V ≘ V2 & ⦃G, L⦄ ⊢ W1 ⬈[Rt, cW, h] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ⬈[Rt, cT, h] T2 &
- U1 = â\93\93{p}W1.T1 & U2 = â\93\93{p}W2.â\93\90V2.T2 & c = ((â\86\93cV)â\88¨(â\86\93cW)∨cT)+𝟙𝟘.
+lemma cpg_inv_appl1: ∀Rt,c,h,G,L,V1,U1,U2. ⦃G,L⦄ ⊢ ⓐV1.U1 ⬈[Rt,c,h] U2 →
+ ∨∨ ∃∃cV,cT,V2,T2. ⦃G,L⦄ ⊢ V1 ⬈[Rt,cV,h] V2 & ⦃G,L⦄ ⊢ U1 ⬈[Rt,cT,h] T2 &
+ U2 = â\93\90V2.T2 & c = ((â\86\95*cV)∨cT)
+ | ∃∃cV,cW,cT,p,V2,W1,W2,T1,T2. ⦃G,L⦄ ⊢ V1 ⬈[Rt,cV,h] V2 & ⦃G,L⦄ ⊢ W1 ⬈[Rt,cW,h] W2 & ⦃G,L.ⓛW1⦄ ⊢ T1 ⬈[Rt,cT,h] T2 &
+ U1 = â\93\9b{p}W1.T1 & U2 = â\93\93{p}â\93\9dW2.V2.T2 & c = ((â\86\95*cV)â\88¨(â\86\95*cW)∨cT)+𝟙𝟘
+ | ∃∃cV,cW,cT,p,V,V2,W1,W2,T1,T2. ⦃G,L⦄ ⊢ V1 ⬈[Rt,cV,h] V & ⇧*[1] V ≘ V2 & ⦃G,L⦄ ⊢ W1 ⬈[Rt,cW,h] W2 & ⦃G,L.ⓓW1⦄ ⊢ T1 ⬈[Rt,cT,h] T2 &
+ U1 = â\93\93{p}W1.T1 & U2 = â\93\93{p}W2.â\93\90V2.T2 & c = ((â\86\95*cV)â\88¨(â\86\95*cW)∨cT)+𝟙𝟘.