/4 width=5 by snv_bind, drop_skip/
| #a #G #K #V #W0 #T #U0 #l #_ #_ #HVW0 #HTU0 #IHV #IHT #L #s #d #e #HLK #X #H
elim (lift_inv_flat1 … H) -H #W #U #HVW #HTU #H destruct
- elim (lift_total W0 d e) #W1 #HW01
- elim (lift_total U0 (d+1) e) #U1 #HU01
- @(snv_appl … a … W1 … U1 l) [1,2,3: /2 width=10 by scpds_lift/ ] -IHV -IHT
- @(scpds_lift … HTU0 … HLK … HTU) /2 width=1 by lift_bind/ (**) (* full auto raises typechecker failure *)
+ elim (lift_total W0 d e)
+ elim (lift_total U0 (d+1) e)
+ /4 width=17 by snv_appl, scpds_lift, lift_bind/
| #G #K #V #T #U0 #_ #_ #HVU0 #HTU0 #IHV #IHT #L #s #d #e #HLK #X #H
elim (lift_inv_flat1 … H) -H #W #U #HVW #HTU #H destruct
elim (lift_total U0 d e)
/4 width=5 by snv_bind, drop_skip/
| #a #G #L #W #W1 #U #U1 #l #_ #_ #HW1 #HU1 #IHW #IHU #K #s #d #e #HLK #X #H
elim (lift_inv_flat2 … H) -H #V #T #HVW #HTU #H destruct
- elim (scpds_inv_lift1 … HW1 … HLK … HVW) -HW1 #W0 #HW01 #HVW0
+ elim (scpds_inv_lift1 … HW1 … HLK … HVW) -HW1 #W0 #HW01 #HVW0
elim (scpds_inv_lift1 … HU1 … HLK … HTU) -HU1 #X #H #HTU0
elim (lift_inv_bind2 … H) -H #Y #U0 #HY #HU01 #H destruct
lapply (lift_inj … HY … HW01) -HY #H destruct
theorem scpes_canc_sn: ∀h,g,G,L,T,T1,l,l1. ⦃G, L⦄ ⊢ T •*⬌*[h, g, l, l1] T1 →
∀T2,l2. ⦃G, L⦄ ⊢ T •*⬌*[h, g, l, l2] T2 → ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, l1, l2] T2.
-#h #g #G #L #T #T1 #l #l1 #HT1
-@scpes_trans /2 width=1 by scpes_sym/ (**) (* full auto raises NTypeChecker failure *)
-qed-.
+/3 width=4 by scpes_trans, scpes_sym/ qed-.
theorem scpes_canc_dx: ∀h,g,G,L,T1,T,l1,l. ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, l1, l] T →
∀T2,l2. ⦃G, L⦄ ⊢ T2 •*⬌*[h, g, l2, l] T → ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, l1, l2] T2.
-#h #g #G #L #T1 #T #l1 #l #HT1 #T2 #l2 #HT2
-@(scpes_trans … HT1) -T1 -l1 /2 width=1 by scpes_sym/ (**) (* full auto raises NTypeChecker failure *)
-qed-.
+/3 width=4 by scpes_trans, scpes_sym/ qed-.
]
class "blue"
[ { "equivalence" * } {
- [ { "decomposed extended equivalence" * } {
+ [ { "decomposed rt-equivalence" * } {
[ "scpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?,?,?] ? )" "scpes_aaa" + "scpes_cpcs" + "scpes_scpes" * ]
}
]
]
class "cyan"
[ { "computation" * } {
- [ { "evaluation for context-sensitive extended reduction" * } {
+ [ { "evaluation for context-sensitive rt-reduction" * } {
[ "cpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ )" * ]
}
]
[ "fsb ( ⦃?,?⦄ ⊢ ⦥[?,?] ? )" "fsb_alt ( ⦃?,?⦄ ⊢ ⦥⦥[?,?] ? )" "fsb_aaa" + "fsb_csx" * ]
}
]
- [ { "strongly normalizing extended computation" * } {
+ [ { "strongly normalizing rt-computation" * } {
[ "lcosx ( ? ⊢ ~⬊*[?,?,?] ? )" "lcosx_cpx" * ]
[ "lsx ( ? ⊢ ⬊*[?,?,?,?] ? )" "lsx_alt ( ? ⊢ ⬊⬊*[?,?,?,?] ? )" "lsx_drop" + "lsx_lpx" + "lsx_lpxs" + "llsx_csx" * ]
[ "csx_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )" "csx_tsts_vector" + "csx_aaa" * ]
[ "fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )" "fpbs_lift" + "fpbs_aaa" + "fpbs_fpb" + "fpbs_fpbs" * ]
}
]
- [ { "decomposed extended computation" * } {
+ [ { "decomposed rt-computation" * } {
[ "scpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?,?] ? )" "scpds_lift" + "scpds_aaa" + "scpds_scpds" * ]
}
]
- [ { "context-sensitive extended computation" * } {
+ [ { "context-sensitive rt-computation" * } {
[ "lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )" "lpxs_drop" + "lpxs_lleq" + "lpxs_aaa" + "lpxs_cpxs" + "lpxs_lpxs" * ]
[ "cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )" "cpxs_tsts" + "cpxs_tsts_vector" + "cpxs_leq" + "cpxs_lift" + "cpxs_lleq" + "cpxs_aaa" + "cpxs_cpxs" * ]
}
[ "fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpb_lift" + "fpb_lleq" + "fpb_fleq" * ]
}
]
- [ { "normal forms for context-sensitive extended reduction" * } {
+ [ { "normal forms for context-sensitive rt-reduction" * } {
[ "cnx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐍⦃?⦄ )" "cnx_lift" + "cnx_crx" + "cnx_cix" * ]
}
]
- [ { "context-sensitive extended reduction" * } {
+ [ { "context-sensitive rt-reduction" * } {
[ "lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lpx_drop" + "lpx_frees" + "lpx_lleq" + "lpx_aaa" * ]
[ "cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )" "cpx_leq" + "cpx_lift" + "cpx_llpx_sn" + "cpx_lleq" + "cpx_cix" * ]
}
]
- [ { "irreducible forms for context-sensitive extended reduction" * } {
+ [ { "irreducible forms for context-sensitive rt-reduction" * } {
[ "cix ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐈⦃?⦄ )" "cix_lift" * ]
}
]
- [ { "reducible forms for context-sensitive extended reduction" * } {
+ [ { "reducible forms for context-sensitive rt-reduction" * } {
[ "crx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐑⦃?⦄ )" "crx_lift" * ]
}
]
[ "frees ( ? ⊢ ? ϵ 𝐅*[?]⦃?⦄ )" "frees_append" + "frees_leq" + "frees_lift" * ]
}
]
- [ { "contxt-sensitive extended multiple substitution" * } {
+ [ { "contxt-sensitive multiple rt-substitution" * } {
[ "cpys ( ⦃?,?⦄ ⊢ ? ▶*[?,?] ? )" "cpys_alt ( ⦃?,?⦄ ⊢ ? ▶▶*[?,?] ? )" "cpys_lift" + "cpys_cpys" * ]
}
]
[ "gget ( ⬇[?] ? ≡ ? )" "gget_gget" * ]
}
]
- [ { "contxt-sensitive extended ordinary substitution" * } {
+ [ { "contxt-sensitive ordinary rt-substitution" * } {
[ "cpy ( ⦃?,?⦄ ⊢ ? ▶[?,?] ? )" "cpy_lift" + "cpy_nlift" + "cpy_cpy" * ]
}
]
- [ { "local env. ref. for extended substitution" * } {
+ [ { "local env. ref. for rt-substitution" * } {
[ "lsuby ( ? ⊆[?,?] ? )" "lsuby_lsuby" * ]
}
]