lemma tpr_conf_lref_lref: ∀i. ∃∃X. #i ⇒ X & #i ⇒ X.
/2/ qed.
-lemma tpr_conf_bind_bind:
- ∀I,V0,V1,T0,T1,V2,T2. (
- ∀X0:term. #X0 < #V0 + #T0 + 1 →
- ∀X1,X2. X0 ⇒ X1 → X0 ⇒ X2 →
- ∃∃X. X1 ⇒ X & X2 ⇒ X
- ) →
- V0 ⇒ V1 → V0 ⇒ V2 → T0 ⇒ T1 → T0 ⇒ T2 →
- ∃∃X. 𝕓{I} V1. T1 ⇒ X & 𝕓{I} V2. T2 ⇒ X.
-#I #V0 #V1 #T0 #T1 #V2 #T2 #IH #HV01 #HV02 #HT01 #HT02
-elim (IH … HV01 … HV02) -HV01 HV02 // #V #HV1 #HV2
-elim (IH … HT01 … HT02) -HT01 HT02 IH /3 width=5/
-qed.
-
-lemma tpr_conf_bind_delta:
- ∀V0,V1,T0,T1,V2,T2,T. (
- ∀X0:term. #X0 < #V0 + #T0 + 1 →
- ∀X1,X2. X0 ⇒ X1 → X0 ⇒ X2 →
- ∃∃X. X1 ⇒ X & X2 ⇒ X
- ) →
- V0 ⇒ V1 → V0 ⇒ V2 →
- T0 ⇒ T1 → T0 ⇒ T2 → ⋆. 𝕓{Abbr} V2 ⊢ T2 [O,1] ≫ T →
- ∃∃X. 𝕓{Abbr} V1. T1 ⇒ X & 𝕓{Abbr} V2. T ⇒ X.
-#V0 #V1 #T0 #T1 #V2 #T2 #T #IH #HV01 #HV02 #HT01 #HT02 #HT2
-elim (IH … HV01 … HV02) -HV01 HV02 // #V #HV1 #HV2
-elim (IH … HT01 … HT02) -HT01 HT02 IH // -V0 T0 #T0 #HT10 #HT20
-elim (tpr_tps_bind … HV2 HT20 … HT2) -HT20 HT2 /3 width=5/
-qed.
-
-lemma tpr_conf_bind_zeta:
- ∀X2,V0,V1,T0,T1,T. (
- ∀X0:term. #X0 < #V0 + #T0 +1 →
- ∀X1,X2. X0 ⇒ X1 → X0 ⇒ X2 →
- ∃∃X. X1 ⇒ X & X2 ⇒ X
- ) →
- V0 ⇒ V1 → T0 ⇒ T1 → T ⇒ X2 → ↑[O, 1] T ≡ T0 →
- ∃∃X. 𝕓{Abbr} V1. T1 ⇒ X & X2 ⇒ X.
-#X2 #V0 #V1 #T0 #T1 #T #IH #HV01 #HT01 #HTX2 #HT0
-elim (tpr_inv_lift … HT01 … HT0) -HT01 #U #HUT1 #HTU
-lapply (tw_lift … HT0) -HT0 #HT0
-elim (IH … HTX2 … HTU) -HTX2 HTU IH /3/
-qed.
-
lemma tpr_conf_flat_flat:
∀I,V0,V1,T0,T1,V2,T2. (
∀X0:term. #X0 < #V0 + #T0 + 1 →
elim (lift_total VV 0 1) #VVV #HVV
lapply (tpr_lift … HVV2 … HV2 … HVV) #HVVV
elim (tpr_inv_abbr1 … H) -H *
-(* case 1: bind *)
-[ -HV2 HVV2 #WW #UU #HWW0 #HUU0 #H destruct -T1;
- elim (IH … HW02 … HWW0) -HW02 HWW0 // #W #HW2 #HWW
- elim (IH … HU02 … HUU0) -HU02 HUU0 IH // #U #HU2 #HUU
- @ex2_1_intro [2: @tpr_theta |1:skip |3: @tpr_bind ] /2 width=7/ (**) (* /4 width=7/ is too slow *)
-(* case 2: delta *)
-| -HV2 HVV2 #WW2 #UU2 #UU #HWW2 #HUU02 #HUU2 #H destruct -T1;
+(* case 1: delta *)
+[ -HV2 HVV2 #WW2 #UU2 #UU #HWW2 #HUU02 #HUU2 #H destruct -T1;
elim (IH … HW02 … HWW2) -HW02 HWW2 // #W #HW02 #HWW2
elim (IH … HU02 … HUU02) -HU02 HUU02 IH // #U #HU2 #HUUU2
elim (tpr_tps_bind … HWW2 HUUU2 … HUU2) -HUU2 HUUU2 #UUU #HUUU2 #HUUU1
qed.
lemma tpr_conf_delta_delta:
- ∀V0,V1,T0,T1,TT1,V2,T2,TT2. (
+ ∀I1,V0,V1,T0,T1,TT1,V2,T2,TT2. (
∀X0:term. #X0 < #V0 +#T0 + 1→
∀X1,X2. X0 ⇒ X1 → X0 ⇒ X2 →
∃∃X. X1 ⇒ X & X2 ⇒ X
) →
V0 ⇒ V1 → V0 ⇒ V2 → T0 ⇒ T1 → T0 ⇒ T2 →
- ⋆. 𝕓{Abbr} V1 ⊢ T1 [O, 1] ≫ TT1 →
- ⋆. 𝕓{Abbr} V2 ⊢ T2 [O, 1] ≫ TT2 →
- ∃∃X. 𝕓{Abbr} V1. TT1 ⇒ X & 𝕓{Abbr} V2. TT2 ⇒ X.
-#V0 #V1 #T0 #T1 #TT1 #V2 #T2 #TT2 #IH #HV01 #HV02 #HT01 #HT02 #HTT1 #HTT2
+ ⋆. 𝕓{I1} V1 ⊢ T1 [O, 1] ≫ TT1 →
+ ⋆. 𝕓{I1} V2 ⊢ T2 [O, 1] ≫ TT2 →
+ ∃∃X. 𝕓{I1} V1. TT1 ⇒ X & 𝕓{I1} V2. TT2 ⇒ X.
+#I1 #V0 #V1 #T0 #T1 #TT1 #V2 #T2 #TT2 #IH #HV01 #HV02 #HT01 #HT02 #HTT1 #HTT2
elim (IH … HV01 … HV02) -HV01 HV02 // #V #HV1 #HV2
elim (IH … HT01 … HT02) -HT01 HT02 IH // #T #HT1 #HT2
elim (tpr_tps_bind … HV1 HT1 … HTT1) -HT1 HTT1 #U1 #TTU1 #HTU1
lapply (tpr_inv_lref1 … H1) -H1
(* case 2: lref, lref *)
#H1 destruct -X2 //
-| #I #V0 #V1 #T0 #T1 #HV01 #HT01 #H1 #H2 destruct -Y0;
- elim (tpr_inv_bind1 … H1) -H1 *
-(* case 3: bind, bind *)
- [ #V2 #T2 #HV02 #HT02 #H destruct -X2
- /3 width=7 by tpr_conf_bind_bind/ (**) (* /3 width=7/ is too slow *)
-(* case 4: bind, delta *)
- | #V2 #T2 #T #HV02 #HT02 #HT2 #H1 #H2 destruct -X2 I
- /3 width=9 by tpr_conf_bind_delta/ (**) (* /3 width=9/ is too slow *)
-(* case 5: bind, zeta *)
- | #T #HT0 #HTX2 #H destruct -I
- /3 width=8 by tpr_conf_bind_zeta/ (**) (* /3 width=8/ is too slow *)
- ]
| #I #V0 #V1 #T0 #T1 #HV01 #HT01 #H1 #H2 destruct -Y0;
elim (tpr_inv_flat1 … H1) -H1 *
-(* case 6: flat, flat *)
+(* case 3: flat, flat *)
[ #V2 #T2 #HV02 #HT02 #H destruct -X2
/3 width=7 by tpr_conf_flat_flat/ (**) (* /3 width=7/ is too slow *)
-(* case 7: flat, beta *)
+(* case 4: flat, beta *)
| #V2 #W #U0 #T2 #HV02 #HT02 #H1 #H2 #H3 destruct -T0 X2 I
/3 width=8 by tpr_conf_flat_beta/ (**) (* /3 width=8/ is too slow *)
-(* case 8: flat, theta *)
+(* case 5: flat, theta *)
| #V2 #V #W0 #W2 #U0 #U2 #HV02 #HW02 #HT02 #HV2 #H1 #H2 #H3 destruct -T0 X2 I
/3 width=11 by tpr_conf_flat_theta/ (**) (* /3 width=11/ is too slow *)
-(* case 9: flat, tau *)
+(* case 6: flat, tau *)
| #HT02 #H destruct -I
/3 width=6 by tpr_conf_flat_cast/ (**) (* /3 width=6/ is too slow *)
]
| #V0 #V1 #W0 #T0 #T1 #HV01 #HT01 #H1 #H2 destruct -Y0;
elim (tpr_inv_appl1 … H1) -H1 *
-(* case 10: beta, flat (repeated) *)
+(* case 7: beta, flat (repeated) *)
[ #V2 #T2 #HV02 #HT02 #H destruct -X2
@ex2_1_comm /3 width=8 by tpr_conf_flat_beta/
-(* case 11: beta, beta *)
+(* case 8: beta, beta *)
| #V2 #WW0 #TT0 #T2 #HV02 #HT02 #H1 #H2 destruct -W0 T0 X2
/3 width=8 by tpr_conf_beta_beta/ (**) (* /3 width=8/ is too slow *)
-(* case 12, beta, theta (excluded) *)
+(* case 9, beta, theta (excluded) *)
| #V2 #VV2 #WW0 #W2 #TT0 #T2 #_ #_ #_ #_ #H destruct
]
-| #V0 #V1 #T0 #T1 #TT1 #HV01 #HT01 #HTT1 #H1 #H2 destruct -Y0;
- elim (tpr_inv_abbr1 … H1) -H1 *
-(* case 13: delta, bind (repeated) *)
- [ #V2 #T2 #HV02 #T02 #H destruct -X2
- @ex2_1_comm /3 width=9 by tpr_conf_bind_delta/
-(* case 14: delta, delta *)
- | #V2 #T2 #TT2 #HV02 #HT02 #HTT2 #H destruct -X2
+| #I1 #V0 #V1 #T0 #T1 #TT1 #HV01 #HT01 #HTT1 #H1 #H2 destruct -Y0;
+ elim (tpr_inv_bind1 … H1) -H1 *
+(* case 10: delta, delta *)
+ [ #V2 #T2 #TT2 #HV02 #HT02 #HTT2 #H destruct -X2
/3 width=11 by tpr_conf_delta_delta/ (**) (* /3 width=11/ is too slow *)
-(* case 15: delta, zata *)
- | #T2 #HT20 #HTX2
+(* case 11: delta, zata *)
+ | #T2 #HT20 #HTX2 #H destruct -I1;
/3 width=10 by tpr_conf_delta_zeta/ (**) (* /3 width=10/ is too slow *)
]
| #VV1 #V0 #V1 #W0 #W1 #T0 #T1 #HV01 #HVV1 #HW01 #HT01 #H1 #H2 destruct -Y0;
elim (tpr_inv_appl1 … H1) -H1 *
-(* case 16: theta, flat (repeated) *)
+(* case 12: theta, flat (repeated) *)
[ #V2 #T2 #HV02 #HT02 #H destruct -X2
@ex2_1_comm /3 width=11 by tpr_conf_flat_theta/
-(* case 17: theta, beta (repeated) *)
+(* case 13: theta, beta (repeated) *)
| #V2 #WW0 #TT0 #T2 #_ #_ #H destruct
-(* case 18: theta, theta *)
+(* case 14: theta, theta *)
| #V2 #VV2 #WW0 #W2 #TT0 #T2 #V02 #HW02 #HT02 #HVV2 #H1 #H2 destruct -W0 T0 X2
- /3 width=14 by tpr_conf_theta_theta/ (**) (* /3 width=14/ is too slow *)
+ /3 width=14 by tpr_conf_theta_theta/ (**) (* /3 width=14/ is too slow *)
]
| #V0 #TT0 #T0 #T1 #HTT0 #HT01 #H1 #H2 destruct -Y0;
elim (tpr_inv_abbr1 … H1) -H1 *
-(* case 19: zeta, bind (repeated) *)
- [ #V2 #T2 #HV02 #T02 #H destruct -X2
- @ex2_1_comm /3 width=8 by tpr_conf_bind_zeta/
-(* case 20: zeta, delta (repeated) *)
- | #V2 #T2 #TT2 #HV02 #HT02 #HTT2 #H destruct -X2
+(* case 15: zeta, delta (repeated) *)
+ [ #V2 #T2 #TT2 #HV02 #HT02 #HTT2 #H destruct -X2
@ex2_1_comm /3 width=10 by tpr_conf_delta_zeta/
-(* case 21: zeta, zeta *)
+(* case 16: zeta, zeta *)
| #T2 #HTT20 #HTX2
/3 width=9 by tpr_conf_zeta_zeta/ (**) (* /3 width=9/ is too slow *)
]
| #V0 #T0 #T1 #HT01 #H1 #H2 destruct -Y0;
elim (tpr_inv_cast1 … H1) -H1
-(* case 22: tau, flat (repeated) *)
+(* case 17: tau, flat (repeated) *)
[ * #V2 #T2 #HV02 #HT02 #H destruct -X2
@ex2_1_comm /3 width=6 by tpr_conf_flat_cast/
-(* case 23: tau, tau *)
+(* case 18: tau, tau *)
| #HT02
/2 by tpr_conf_tau_tau/
]
projects / helm.git / blobdiff