∀G0,L0,i. (
∀G,L,T. ⦃G0,L0,#i⦄ ⬂+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
) →
- â\88\80K0,V0. â¬\87*[i] L0 ≘ K0.ⓓV0 →
- â\88\80V2. â¦\83G0,K0â¦\84 â\8a¢ V0 â\9e¡[h] V2 â\86\92 â\88\80T2. â¬\86*[↑i] V2 ≘ T2 →
+ â\88\80K0,V0. â\87©*[i] L0 ≘ K0.ⓓV0 →
+ â\88\80V2. â¦\83G0,K0â¦\84 â\8a¢ V0 â\9e¡[h] V2 â\86\92 â\88\80T2. â\87§*[↑i] V2 ≘ T2 →
∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
∃∃T. ⦃G0,L1⦄ ⊢ #i ➡[h] T & ⦃G0,L2⦄ ⊢ T2 ➡[h] T.
#h #G0 #L0 #i #IH #K0 #V0 #HLK0 #V2 #HV02 #T2 #HVT2 #L1 #HL01 #L2 #HL02
∀G0,L0,i. (
∀G,L,T. ⦃G0,L0,#i⦄ ⬂+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
) →
- â\88\80K0,V0. â¬\87*[i] L0 ≘ K0.ⓓV0 →
- â\88\80V1. â¦\83G0,K0â¦\84 â\8a¢ V0 â\9e¡[h] V1 â\86\92 â\88\80T1. â¬\86*[↑i] V1 ≘ T1 →
- â\88\80KX,VX. â¬\87*[i] L0 ≘ KX.ⓓVX →
- â\88\80V2. â¦\83G0,KXâ¦\84 â\8a¢ VX â\9e¡[h] V2 â\86\92 â\88\80T2. â¬\86*[↑i] V2 ≘ T2 →
+ â\88\80K0,V0. â\87©*[i] L0 ≘ K0.ⓓV0 →
+ â\88\80V1. â¦\83G0,K0â¦\84 â\8a¢ V0 â\9e¡[h] V1 â\86\92 â\88\80T1. â\87§*[↑i] V1 ≘ T1 →
+ â\88\80KX,VX. â\87©*[i] L0 ≘ KX.ⓓVX →
+ â\88\80V2. â¦\83G0,KXâ¦\84 â\8a¢ VX â\9e¡[h] V2 â\86\92 â\88\80T2. â\87§*[↑i] V2 ≘ T2 →
∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
∃∃T. ⦃G0,L1⦄ ⊢ T1 ➡[h] T & ⦃G0,L2⦄ ⊢ T2 ➡[h] T.
#h #G0 #L0 #i #IH #K0 #V0 #HLK0 #V1 #HV01 #T1 #HVT1
∀G,L,T. ⦃G0,L0,+ⓓV0.T0⦄ ⬂+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
) →
∀V1. ⦃G0,L0⦄ ⊢ V0 ➡[h] V1 → ∀T1. ⦃G0,L0.ⓓV0⦄ ⊢ T0 ➡[h] T1 →
- â\88\80T2. â¬\86*[1]T2 ≘ T0 → ∀X2. ⦃G0,L0⦄ ⊢ T2 ➡[h] X2 →
+ â\88\80T2. â\87§*[1]T2 ≘ T0 → ∀X2. ⦃G0,L0⦄ ⊢ T2 ➡[h] X2 →
∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
∃∃T. ⦃G0,L1⦄ ⊢ +ⓓV1.T1 ➡[h] T & ⦃G0,L2⦄ ⊢ X2 ➡[h] T.
#h #G0 #L0 #V0 #T0 #IH #V1 #HV01 #T1 #HT01
∀G0,L0,V0,T0. (
∀G,L,T. ⦃G0,L0,+ⓓV0.T0⦄ ⬂+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
) →
- â\88\80T1. â¬\86*[1] T1 ≘ T0 → ∀X1. ⦃G0,L0⦄ ⊢ T1 ➡[h] X1 →
- â\88\80T2. â¬\86*[1] T2 ≘ T0 → ∀X2. ⦃G0,L0⦄ ⊢ T2 ➡[h] X2 →
+ â\88\80T1. â\87§*[1] T1 ≘ T0 → ∀X1. ⦃G0,L0⦄ ⊢ T1 ➡[h] X1 →
+ â\88\80T2. â\87§*[1] T2 ≘ T0 → ∀X2. ⦃G0,L0⦄ ⊢ T2 ➡[h] X2 →
∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
∃∃T. ⦃G0,L1⦄ ⊢ X1 ➡[h] T & ⦃G0,L2⦄ ⊢ X2 ➡[h] T.
#h #G0 #L0 #V0 #T0 #IH #T1 #HT10 #X1 #HTX1
∀G,L,T. ⦃G0,L0,ⓐV0.ⓓ{p}W0.T0⦄ ⬂+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
) →
∀V1. ⦃G0,L0⦄ ⊢ V0 ➡[h] V1 → ∀T1. ⦃G0,L0⦄ ⊢ ⓓ{p}W0.T0 ➡[h] T1 →
- â\88\80V2. â¦\83G0,L0â¦\84 â\8a¢ V0 â\9e¡[h] V2 â\86\92 â\88\80U2. â¬\86*[1] V2 ≘ U2 →
+ â\88\80V2. â¦\83G0,L0â¦\84 â\8a¢ V0 â\9e¡[h] V2 â\86\92 â\88\80U2. â\87§*[1] V2 ≘ U2 →
∀W2. ⦃G0,L0⦄ ⊢ W0 ➡[h] W2 → ∀T2. ⦃G0,L0.ⓓW0⦄ ⊢ T0 ➡[h] T2 →
∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
∃∃T. ⦃G0,L1⦄ ⊢ ⓐV1.T1 ➡[h] T & ⦃G0,L2⦄ ⊢ ⓓ{p}W2.ⓐU2.T2 ➡[h] T.
∀p,G0,L0,V0,W0,T0. (
∀G,L,T. ⦃G0,L0,ⓐV0.ⓓ{p}W0.T0⦄ ⬂+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
) →
- â\88\80V1. â¦\83G0,L0â¦\84 â\8a¢ V0 â\9e¡[h] V1 â\86\92 â\88\80U1. â¬\86*[1] V1 ≘ U1 →
+ â\88\80V1. â¦\83G0,L0â¦\84 â\8a¢ V0 â\9e¡[h] V1 â\86\92 â\88\80U1. â\87§*[1] V1 ≘ U1 →
∀W1. ⦃G0,L0⦄ ⊢ W0 ➡[h] W1 → ∀T1. ⦃G0,L0.ⓓW0⦄ ⊢ T0 ➡[h] T1 →
- â\88\80V2. â¦\83G0,L0â¦\84 â\8a¢ V0 â\9e¡[h] V2 â\86\92 â\88\80U2. â¬\86*[1] V2 ≘ U2 →
+ â\88\80V2. â¦\83G0,L0â¦\84 â\8a¢ V0 â\9e¡[h] V2 â\86\92 â\88\80U2. â\87§*[1] V2 ≘ U2 →
∀W2. ⦃G0,L0⦄ ⊢ W0 ➡[h] W2 → ∀T2. ⦃G0,L0.ⓓW0⦄ ⊢ T0 ➡[h] T2 →
∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
∃∃T. ⦃G0,L1⦄ ⊢ ⓓ{p}W1.ⓐU1.T1 ➡[h] T & ⦃G0,L2⦄ ⊢ ⓓ{p}W2.ⓐU2.T2 ➡[h] T.