lemma csx_lpx_conf: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 →
∀T. ⦃G, L1⦄ ⊢ ⬊*[h, g] T → ⦃G, L2⦄ ⊢ ⬊*[h, g] T.
-#h #g #G #L1 #L2 #HL12 #T #H @(csx_ind_alt … H) -T #T #_ #IHT
-@csx_intro #T0 #HLT0 #HT0
-@IHT /2 width=2/ -IHT -HT0 /2 width=3 by lpx_cpx_trans/
-qed.
+#h #g #G #L1 #L2 #HL12 #T #H @(csx_ind_alt … H) -T
+/4 width=3 by csx_intro, lpx_cpx_trans/
+qed-.
lemma csx_abst: ∀h,g,a,G,L,W. ⦃G, L⦄ ⊢ ⬊*[h, g] W →
∀T. ⦃G, L.ⓛW⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⬊*[h, g] ⓛ{a}W.T.
#W0 #T0 #HLW0 #HLT0 #H destruct
elim (eq_false_inv_tpair_sn … H2) -H2
[ -IHT #H lapply (csx_cpx_trans … HLT0) // -HT
- #HT0 lapply (csx_lpx_conf … (L.ⓛW0) … HT0) -HT0 /2 width=1/ /3 width=1/
-| -IHW -HLW0 -HT * #H destruct /3 width=1/
+ #HT0 lapply (csx_lpx_conf … (L.ⓛW0) … HT0) -HT0 /3 width=1 by lpx_pair/
+| -IHW -HLW0 -HT * #H destruct /3 width=1 by/
]
qed.
elim (cpx_inv_abbr1 … H1) -H1 *
[ #V1 #T1 #HLV1 #HLT1 #H destruct
elim (eq_false_inv_tpair_sn … H2) -H2
- [ #HV1 @IHV // /2 width=1/ -HV1
- @(csx_lpx_conf … (L.ⓓV)) /2 width=1/ -HLV1 /2 width=3 by csx_cpx_trans/
- | -IHV -HLV1 * #H destruct /3 width=1/
+ [ /4 width=5 by csx_cpx_trans, csx_lpx_conf, lpx_pair/
+ | -IHV -HLV1 * #H destruct /3 width=1 by cpx_cpxs/
]
-| -IHV -IHT -H2 #T0 #HLT0 #HT0
- lapply (csx_cpx_trans … HT … HLT0) -T #HLT0
- lapply (csx_inv_lift … HLT0 … HT0) -T0 /2 width=3/
+| -IHV -IHT -H2
+ /3 width=8 by csx_cpx_trans, csx_inv_lift, ldrop_drop/
]
qed.
elim (cpx_inv_appl1 … H1) -H1 *
[ -HT1 #V0 #Y #HLV0 #H #H0 destruct
elim (cpx_inv_abst1 … H) -H #W0 #T0 #HLW0 #HLT0 #H destruct
- @IHT1 -IHT1 [4: // | skip |3: #H destruct /2 width=1/ ] -H2
- lapply (lsubr_cpx_trans … HLT0 (L.ⓓⓝW.V) ?) -HLT0 [ /2 width=1/ ] /3 width=1/
+ @IHT1 -IHT1 [4: // | skip |3: #H destruct /2 width=1 by/ ] -H2
+ lapply (lsubr_cpx_trans … HLT0 (L.ⓓⓝW.V) ?) -HLT0 /3 width=1 by cpx_bind, cpx_flat, lsubr_abst/
| -IHT1 -H2 #b #V0 #W0 #W2 #T0 #T2 #HLV0 #HLW02 #HLT02 #H1 #H3 destruct
- lapply (lsubr_cpx_trans … HLT02 (L.ⓓⓝW0.V) ?) -HLT02 [ /2 width=1/ ] #HT02
- @(csx_cpx_trans … HT1) -HT1 /3 width=1/
+ lapply (lsubr_cpx_trans … HLT02 (L.ⓓⓝW0.V) ?) -HLT02
+ /4 width=5 by csx_cpx_trans, cpx_bind, cpx_flat, lsubr_abst/
| -HT1 -IHT1 -H2 #b #V0 #V1 #W0 #W1 #T0 #T3 #_ #_ #_ #_ #H destruct
]
qed-.
| * #_ #H elim H //
]
| -H -HVT #H
- lapply (cpx_lift … HLV10 (L. ⓓV) … HV12 … HV04) -HLV10 -HV12 /2 width=1/ #HV24
- @(IHVT … H … HV04) -IHVT // -H -HV04 /4 width=1/
+ lapply (cpx_lift … HLV10 (L.ⓓV) (Ⓣ) … HV12 … HV04) -HLV10 -HV12 /2 width=1 by ldrop_drop/ #HV24
+ @(IHVT … H … HV04) -IHVT /4 width=1 by cpx_cpxs, cpx_bind, cpx_flat/
]
| -H -IHVT #T0 #HLT0 #HT0 #H0 destruct
- lapply (csx_cpx_trans … HVT (ⓐV2.T0) ?) /2 width=1/ -T #HVT0
- lapply (csx_inv_lift … L … 1 HVT0 ? ? ?) -HVT0 [ /2 width=4/ |2,3: skip | /2 width=1/ ] -V2 -T0 #HVY
- @(csx_cpx_trans … HVY) /2 width=1/
+ lapply (csx_cpx_trans … HVT (ⓐV2.T0) ?) /2 width=1 by cpx_flat/ -T #HVT0
+ lapply (csx_inv_lift … L … (Ⓣ) … 1 HVT0 ? ? ?) -HVT0
+ /3 width=5 by csx_cpx_trans, cpx_pair_sn, ldrop_drop, lift_flat/
]
| -HV -HV12 -HVT -IHVT -H #b #V0 #W0 #W1 #T0 #T1 #_ #_ #_ #H destruct
| -IHVT -H #b #V0 #V3 #W0 #W1 #T0 #T1 #HLV10 #HV03 #HLW01 #HLT01 #H1 #H2 destruct
- lapply (cpx_lift … HLV10 (L. ⓓW0) … HV12 … HV03) -HLV10 -HV12 -HV03 /2 width=1/ #HLV23
+ lapply (cpx_lift … HLV10 (L. ⓓW0) … HV12 … HV03) -HLV10 -HV12 -HV03 /2 width=2 by ldrop_drop/ #HLV23
@csx_abbr /2 width=3 by csx_cpx_trans/ -HV
- @(csx_lpx_conf … (L. ⓓW0)) /2 width=1/ -W1
- @(csx_cpxs_trans … HVT) -HVT /3 width=1/
+ @(csx_lpx_conf … (L.ⓓW0)) /2 width=1 by lpx_pair/ -W1
+ /4 width=5 by csx_cpxs_trans, cpx_cpxs, cpx_flat/
]
qed-.
#V0 #T0 #HLV0 #HLT10 #H0 destruct
elim (eq_false_inv_tpair_sn … H) -H
[ -IHT1 #HV0
- @(csx_cpx_trans … (ⓐV0.T1)) /2 width=1/ -HLT10
- @IHV -IHV // -H1T1 -H3T1 /2 width=1/ -HV0
- #T2 #HLT12 #HT12
- @(csx_cpx_trans … (ⓐV.T2)) /2 width=1/ -HLV0
- @H2T1 -H2T1 // -HLT12 /2 width=1/
+ @(csx_cpx_trans … (ⓐV0.T1)) /2 width=1 by cpx_flat/ -HLT10
+ @IHV -IHV /4 width=3 by csx_cpx_trans, cpx_pair_sn/
| -IHV -H1T1 -HLV0 * #H #H1T10 destruct
elim (tstc_dec T1 T0) #H2T10
- [ @IHT1 -IHT1 // /2 width=1/ -H1T10 /2 width=3/ -H3T1
- #T2 #HLT02 #HT02
- @H2T1 -H2T1 /2 width=3/ -HLT10 -HLT02 /3 width=3/
- | -IHT1 -H3T1 -H1T10
- @H2T1 -H2T1 /2 width=1/
+ [ @IHT1 -IHT1 /4 width=3 by cpxs_strap2, cpxs_strap1, tstc_canc_sn, simple_tstc_repl_dx/
+ | -IHT1 -H3T1 -H1T10 /3 width=1 by cpx_cpxs/
]
]
qed.