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15 include "basic_2/static/ssta_ltpss.ma".
16 include "basic_2/unwind/sstas.ma".
18 (* ITERATED STRATIFIED STATIC TYPE ASSIGNMENTON TERMS ***********************)
20 (* Properties about parallel unfold *****************************************)
22 lemma sstas_ltpss_tpss_conf: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 →
23 ∀L2,d,e. L1 ▶* [d, e] L2 →
24 ∀T2. L2 ⊢ T1 ▶* [d, e] T2 →
25 ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 &
27 #h #g #L1 #T1 #U1 #H @(sstas_ind_alt … H) -T1
28 [ #T1 #HUT1 #L2 #d #e #HL12 #U2 #HU12
29 elim (ssta_ltpss_tpss_conf … HUT1 … HL12 … HU12) -HUT1 -HL12 /3 width=3/
30 | #T0 #U0 #l0 #HTU0 #_ #IHU01 #L2 #d #e #HL12 #T #HT0
31 elim (ssta_ltpss_tpss_conf … HTU0 … HL12 … HT0) -HTU0 -HT0 #U #HTU #HU0
32 elim (IHU01 … HL12 … HU0) -IHU01 -HL12 -U0 /3 width=4/
36 lemma sstas_ltpss_tps_conf: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 →
37 ∀L2,d,e. L1 ▶* [d, e] L2 →
38 ∀T2. L2 ⊢ T1 ▶ [d, e] T2 →
39 ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 & L2 ⊢ U1 ▶* [d, e] U2.
42 lemma sstas_ltpss_conf: ∀h,g,L1,T,U1. ⦃h, L1⦄ ⊢ T •*[g] U1 →
43 ∀L2,d,e. L1 ▶* [d, e] L2 →
44 ∃∃U2. ⦃h, L2⦄ ⊢ T •*[g] U2 & L2 ⊢ U1 ▶* [d, e] U2.
47 lemma sstas_tpss_conf: ∀h,g,L,T1,U1. ⦃h, L⦄ ⊢ T1 •*[g] U1 →
48 ∀T2,d,e. L ⊢ T1 ▶* [d, e] T2 →
49 ∃∃U2. ⦃h, L⦄ ⊢ T2 •*[g] U2 & L ⊢ U1 ▶* [d, e] U2.
52 lemma sstas_tps_conf: ∀h,g,L,T1,U1. ⦃h, L⦄ ⊢ T1 •*[g] U1 →
53 ∀T2,d,e. L ⊢ T1 ▶ [d, e] T2 →
54 ∃∃U2. ⦃h, L⦄ ⊢ T2 •*[g] U2 & L ⊢ U1 ▶* [d, e] U2.