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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/notation/relations/pred_6.ma".
16 include "basic_2/notation/relations/pred_5.ma".
17 include "basic_2/rt_transition/cpg.ma".
19 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
21 (* Basic_2A1: includes: cpr *)
22 definition cpm (n) (h): relation4 genv lenv term term ≝
23 λG,L,T1,T2. ∃∃c. 𝐑𝐓⦃n, c⦄ & ⦃G, L⦄ ⊢ T1 ⬈[c, h] T2.
26 "semi-counted context-sensitive parallel rt-transition (term)"
27 'PRed n h G L T1 T2 = (cpm n h G L T1 T2).
30 "context-sensitive parallel r-transition (term)"
31 'PRed h G L T1 T2 = (cpm O h G L T1 T2).
33 (* Basic properties *********************************************************)
35 lemma cpm_ess: ∀h,G,L,s. ⦃G, L⦄ ⊢ ⋆s ➡[1, h] ⋆(next h s).
36 /2 width=3 by cpg_ess, ex2_intro/ qed.
38 lemma cpm_delta: ∀n,h,G,K,V1,V2,W2. ⦃G, K⦄ ⊢ V1 ➡[n, h] V2 →
39 ⬆*[1] V2 ≡ W2 → ⦃G, K.ⓓV1⦄ ⊢ #0 ➡[n, h] W2.
40 #n #h #G #K #V1 #V2 #W2 *
41 /3 width=5 by cpg_delta, ex2_intro/
44 lemma cpm_ell: ∀n,h,G,K,V1,V2,W2. ⦃G, K⦄ ⊢ V1 ➡[n, h] V2 →
45 ⬆*[1] V2 ≡ W2 → ⦃G, K.ⓛV1⦄ ⊢ #0 ➡[⫯n, h] W2.
46 #n #h #G #K #V1 #V2 #W2 *
47 /3 width=5 by cpg_ell, ex2_intro, isrt_succ/
50 lemma cpm_lref: ∀n,h,I,G,K,V,T,U,i. ⦃G, K⦄ ⊢ #i ➡[n, h] T →
51 ⬆*[1] T ≡ U → ⦃G, K.ⓑ{I}V⦄ ⊢ #⫯i ➡[n, h] U.
52 #n #h #I #G #K #V #T #U #i *
53 /3 width=5 by cpg_lref, ex2_intro/
56 (* Basic_2A1: includes: cpr_bind *)
57 lemma cpm_bind: ∀n,h,p,I,G,L,V1,V2,T1,T2.
58 ⦃G, L⦄ ⊢ V1 ➡[h] V2 → ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ➡[n, h] T2 →
59 ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ➡[n, h] ⓑ{p,I}V2.T2.
60 #n #h #p #I #G #L #V1 #V2 #T1 #T2 * #riV #rhV #HV12 *
61 /5 width=5 by cpg_bind, isrt_plus_O1, isr_shift, ex2_intro/
64 (* Note: cpr_flat: does not hold in basic_1 *)
65 (* Basic_1: includes: pr2_thin_dx *)
66 (* Basic_2A1: includes: cpr_flat *)
67 lemma cpm_flat: ∀n,h,I,G,L,V1,V2,T1,T2.
68 ⦃G, L⦄ ⊢ V1 ➡[h] V2 → ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 →
69 ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ➡[n, h] ⓕ{I}V2.T2.
70 #n #h #I #G #L #V1 #V2 #T1 #T2 * #riV #rhV #HV12 *
71 /5 width=5 by isrt_plus_O1, isr_shift, cpg_flat, ex2_intro/
74 (* Basic_2A1: includes: cpr_zeta *)
75 lemma cpm_zeta: ∀n,h,G,L,V,T1,T,T2. ⦃G, L.ⓓV⦄ ⊢ T1 ➡[n, h] T →
76 ⬆*[1] T2 ≡ T → ⦃G, L⦄ ⊢ +ⓓV.T1 ➡[n, h] T2.
77 #n #h #G #L #V #T1 #T #T2 *
78 /3 width=5 by cpg_zeta, isrt_plus_O2, ex2_intro/
81 (* Basic_2A1: includes: cpr_eps *)
82 lemma cpm_eps: ∀n,h,G,L,V,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 → ⦃G, L⦄ ⊢ ⓝV.T1 ➡[n, h] T2.
83 #n #h #G #L #V #T1 #T2 *
84 /3 width=3 by cpg_eps, isrt_plus_O2, ex2_intro/
87 lemma cpm_ee: ∀n,h,G,L,V1,V2,T. ⦃G, L⦄ ⊢ V1 ➡[n, h] V2 → ⦃G, L⦄ ⊢ ⓝV1.T ➡[⫯n, h] V2.
88 #n #h #G #L #V1 #V2 #T *
89 /3 width=3 by cpg_ee, isrt_succ, ex2_intro/
92 (* Basic_2A1: includes: cpr_beta *)
93 lemma cpm_beta: ∀n,h,p,G,L,V1,V2,W1,W2,T1,T2.
94 ⦃G, L⦄ ⊢ V1 ➡[h] V2 → ⦃G, L⦄ ⊢ W1 ➡[h] W2 → ⦃G, L.ⓛW1⦄ ⊢ T1 ➡[n, h] T2 →
95 ⦃G, L⦄ ⊢ ⓐV1.ⓛ{p}W1.T1 ➡[n, h] ⓓ{p}ⓝW2.V2.T2.
96 #n #h #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 * #riV #rhV #HV12 * #riW #rhW #HW12 *
97 /6 width=7 by cpg_beta, isrt_plus_O2, isrt_plus, isr_shift, ex2_intro/
100 (* Basic_2A1: includes: cpr_theta *)
101 lemma cpm_theta: ∀n,h,p,G,L,V1,V,V2,W1,W2,T1,T2.
102 ⦃G, L⦄ ⊢ V1 ➡[h] V → ⬆*[1] V ≡ V2 → ⦃G, L⦄ ⊢ W1 ➡[h] W2 →
103 ⦃G, L.ⓓW1⦄ ⊢ T1 ➡[n, h] T2 →
104 ⦃G, L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ➡[n, h] ⓓ{p}W2.ⓐV2.T2.
105 #n #h #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 * #riV #rhV #HV1 #HV2 * #riW #rhW #HW12 *
106 /6 width=9 by cpg_theta, isrt_plus_O2, isrt_plus, isr_shift, ex2_intro/
109 (* Basic properties on r-transition *****************************************)
111 (* Basic_1: includes by definition: pr0_refl *)
112 (* Basic_2A1: includes: cpr_atom *)
113 lemma cpr_refl: ∀h,G,L. reflexive … (cpm 0 h G L).
114 /2 width=3 by ex2_intro/ qed.
116 (* Basic_1: was: pr2_head_1 *)
117 lemma cpr_pair_sn: ∀h,I,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 →
118 ∀T. ⦃G, L⦄ ⊢ ②{I}V1.T ➡[h] ②{I}V2.T.
119 #h #I #G #L #V1 #V2 *
120 /3 width=3 by cpg_pair_sn, isr_shift, ex2_intro/
123 (* Basic inversion lemmas ***************************************************)
125 lemma cpm_inv_atom1: ∀n,h,J,G,L,T2. ⦃G, L⦄ ⊢ ⓪{J} ➡[n, h] T2 →
127 | ∃∃s. T2 = ⋆(next h s) & J = Sort s & n = 1
128 | ∃∃K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[n, h] V2 & ⬆*[1] V2 ≡ T2 &
129 L = K.ⓓV1 & J = LRef 0
130 | ∃∃m,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[m, h] V2 & ⬆*[1] V2 ≡ T2 &
131 L = K.ⓛV1 & J = LRef 0 & n = ⫯m
132 | ∃∃I,K,V,T,i. ⦃G, K⦄ ⊢ #i ➡[n, h] T & ⬆*[1] T ≡ T2 &
133 L = K.ⓑ{I}V & J = LRef (⫯i).
134 #n #h #J #G #L #T2 * #c #Hc #H elim (cpg_inv_atom1 … H) -H *
135 [ #H1 #H2 destruct /4 width=1 by isrt_inv_00, or5_intro0, conj/
136 | #s #H1 #H2 #H3 destruct /4 width=3 by isrt_inv_01, or5_intro1, ex3_intro/
137 | #cV #K #V1 #V2 #HV12 #HVT2 #H1 #H2 #H3 destruct
138 /4 width=6 by or5_intro2, ex4_3_intro, ex2_intro/
139 | #cV #K #V1 #V2 #HV12 #HVT2 #H1 #H2 #H3 destruct
140 elim (isrt_inv_plus_SO_dx … Hc) -Hc // #m #Hc #H destruct
141 /4 width=9 by or5_intro3, ex5_4_intro, ex2_intro/
142 | #I #K #V1 #V2 #i #HV2 #HVT2 #H1 #H2 destruct
143 /4 width=9 by or5_intro4, ex4_5_intro, ex2_intro/
147 lemma cpm_inv_sort1: ∀n,h,G,L,T2,s. ⦃G, L⦄ ⊢ ⋆s ➡[n,h] T2 →
149 (T2 = ⋆(next h s) ∧ n = 1).
150 #n #h #G #L #T2 #s * #c #Hc #H elim (cpg_inv_sort1 … H) -H *
152 /4 width=1 by isrt_inv_01, isrt_inv_00, or_introl, or_intror, conj/
155 lemma cpm_inv_zero1: ∀n,h,G,L,T2. ⦃G, L⦄ ⊢ #0 ➡[n, h] T2 →
157 | ∃∃K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[n, h] V2 & ⬆*[1] V2 ≡ T2 &
159 | ∃∃m,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[m, h] V2 & ⬆*[1] V2 ≡ T2 &
161 #n #h #G #L #T2 * #c #Hc #H elim (cpg_inv_zero1 … H) -H *
162 [ #H1 #H2 destruct /4 width=1 by isrt_inv_00, or3_intro0, conj/
163 | #cV #K #V1 #V2 #HV12 #HVT2 #H1 #H2 destruct
164 /4 width=8 by or3_intro1, ex3_3_intro, ex2_intro/
165 | #cV #K #V1 #V2 #HV12 #HVT2 #H1 #H2 destruct
166 elim (isrt_inv_plus_SO_dx … Hc) -Hc // #m #Hc #H destruct
167 /4 width=8 by or3_intro2, ex4_4_intro, ex2_intro/
171 lemma cpm_inv_lref1: ∀n,h,G,L,T2,i. ⦃G, L⦄ ⊢ #⫯i ➡[n, h] T2 →
172 (T2 = #(⫯i) ∧ n = 0) ∨
173 ∃∃I,K,V,T. ⦃G, K⦄ ⊢ #i ➡[n, h] T & ⬆*[1] T ≡ T2 & L = K.ⓑ{I}V.
174 #n #h #G #L #T2 #i * #c #Hc #H elim (cpg_inv_lref1 … H) -H *
175 [ #H1 #H2 destruct /4 width=1 by isrt_inv_00, or_introl, conj/
176 | #I #K #V1 #V2 #HV2 #HVT2 #H1 destruct
177 /4 width=7 by ex3_4_intro, ex2_intro, or_intror/
181 lemma cpm_inv_gref1: ∀n,h,G,L,T2,l. ⦃G, L⦄ ⊢ §l ➡[n, h] T2 → T2 = §l ∧ n = 0.
182 #n #h #G #L #T2 #l * #c #Hc #H elim (cpg_inv_gref1 … H) -H
183 #H1 #H2 destruct /3 width=1 by isrt_inv_00, conj/
186 (* Basic_2A1: includes: cpr_inv_bind1 *)
187 lemma cpm_inv_bind1: ∀n,h,p,I,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ➡[n, h] U2 → (
188 ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ➡[n, h] T2 &
191 ∃∃T. ⦃G, L.ⓓV1⦄ ⊢ T1 ➡[n, h] T & ⬆*[1] U2 ≡ T &
193 #n #h #p #I #G #L #V1 #T1 #U2 * #c #Hc #H elim (cpg_inv_bind1 … H) -H *
194 [ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
195 elim (isrt_inv_plus … Hc) -Hc #nV #nT #HcV #HcT #H destruct
196 elim (isrt_inv_shift … HcV) -HcV #HcV #H destruct
197 /4 width=5 by ex3_2_intro, ex2_intro, or_introl/
198 | #cT #T2 #HT12 #HUT2 #H1 #H2 #H3 destruct
199 /5 width=3 by isrt_inv_plus_O_dx, ex4_intro, ex2_intro, or_intror/
203 (* Basic_1: includes: pr0_gen_abbr pr2_gen_abbr *)
204 (* Basic_2A1: includes: cpr_inv_abbr1 *)
205 lemma cpm_inv_abbr1: ∀n,h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{p}V1.T1 ➡[n, h] U2 → (
206 ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ➡[n, h] T2 &
209 ∃∃T. ⦃G, L.ⓓV1⦄ ⊢ T1 ➡[n, h] T & ⬆*[1] U2 ≡ T & p = true.
210 #n #h #p #G #L #V1 #T1 #U2 * #c #Hc #H elim (cpg_inv_abbr1 … H) -H *
211 [ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
212 elim (isrt_inv_plus … Hc) -Hc #nV #nT #HcV #HcT #H destruct
213 elim (isrt_inv_shift … HcV) -HcV #HcV #H destruct
214 /4 width=5 by ex3_2_intro, ex2_intro, or_introl/
215 | #cT #T2 #HT12 #HUT2 #H1 #H2 destruct
216 /5 width=3 by isrt_inv_plus_O_dx, ex3_intro, ex2_intro, or_intror/
220 (* Basic_1: includes: pr0_gen_abst pr2_gen_abst *)
221 (* Basic_2A1: includes: cpr_inv_abst1 *)
222 lemma cpm_inv_abst1: ∀n,h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ➡[n, h] U2 →
223 ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 ➡[n, h] T2 &
225 #n #h #p #G #L #V1 #T1 #U2 * #c #Hc #H elim (cpg_inv_abst1 … H) -H
226 #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
227 elim (isrt_inv_plus … Hc) -Hc #nV #nT #HcV #HcT #H destruct
228 elim (isrt_inv_shift … HcV) -HcV #HcV #H destruct
229 /3 width=5 by ex3_2_intro, ex2_intro/
232 lemma cpm_inv_flat1: ∀n,h,I,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓕ{I}V1.U1 ➡[n, h] U2 →
233 ∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ U1 ➡[n, h] T2 &
235 | (⦃G, L⦄ ⊢ U1 ➡[n, h] U2 ∧ I = Cast)
236 | ∃∃m. ⦃G, L⦄ ⊢ V1 ➡[m, h] U2 & I = Cast & n = ⫯m
237 | ∃∃p,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ W1 ➡[h] W2 &
238 ⦃G, L.ⓛW1⦄ ⊢ T1 ➡[n, h] T2 &
240 U2 = ⓓ{p}ⓝW2.V2.T2 & I = Appl
241 | ∃∃p,V,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V & ⬆*[1] V ≡ V2 &
242 ⦃G, L⦄ ⊢ W1 ➡[h] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ➡[n, h] T2 &
244 U2 = ⓓ{p}W2.ⓐV2.T2 & I = Appl.
245 #n #h #I #G #L #V1 #U1 #U2 * #c #Hc #H elim (cpg_inv_flat1 … H) -H *
246 [ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
247 elim (isrt_inv_plus … Hc) -Hc #nV #nT #HcV #HcT #H destruct
248 elim (isrt_inv_shift … HcV) -HcV #HcV #H destruct
249 /4 width=5 by or5_intro0, ex3_2_intro, ex2_intro/
250 | #cU #U12 #H1 #H2 destruct
251 /5 width=3 by isrt_inv_plus_O_dx, or5_intro1, conj, ex2_intro/
252 | #cU #H12 #H1 #H2 destruct
253 elim (isrt_inv_plus_SO_dx … Hc) -Hc // #m #Hc #H destruct
254 /4 width=3 by or5_intro2, ex3_intro, ex2_intro/
255 | #cV #cW #cT #p #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 #HT12 #H1 #H2 #H3 #H4 destruct
256 lapply (isrt_inv_plus_O_dx … Hc ?) -Hc // #Hc
257 elim (isrt_inv_plus … Hc) -Hc #n0 #nT #Hc #HcT #H destruct
258 elim (isrt_inv_plus … Hc) -Hc #nV #nW #HcV #HcW #H destruct
259 elim (isrt_inv_shift … HcV) -HcV #HcV #H destruct
260 elim (isrt_inv_shift … HcW) -HcW #HcW #H destruct
261 /4 width=11 by or5_intro3, ex6_6_intro, ex2_intro/
262 | #cV #cW #cT #p #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 #HW12 #HT12 #H1 #H2 #H3 #H4 destruct
263 lapply (isrt_inv_plus_O_dx … Hc ?) -Hc // #Hc
264 elim (isrt_inv_plus … Hc) -Hc #n0 #nT #Hc #HcT #H destruct
265 elim (isrt_inv_plus … Hc) -Hc #nV #nW #HcV #HcW #H destruct
266 elim (isrt_inv_shift … HcV) -HcV #HcV #H destruct
267 elim (isrt_inv_shift … HcW) -HcW #HcW #H destruct
268 /4 width=13 by or5_intro4, ex7_7_intro, ex2_intro/
272 (* Basic_1: includes: pr0_gen_appl pr2_gen_appl *)
273 (* Basic_2A1: includes: cpr_inv_appl1 *)
274 lemma cpm_inv_appl1: ∀n,h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓐ V1.U1 ➡[n, h] U2 →
275 ∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ U1 ➡[n, h] T2 &
277 | ∃∃p,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ W1 ➡[h] W2 &
278 ⦃G, L.ⓛW1⦄ ⊢ T1 ➡[n, h] T2 &
279 U1 = ⓛ{p}W1.T1 & U2 = ⓓ{p}ⓝW2.V2.T2
280 | ∃∃p,V,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V & ⬆*[1] V ≡ V2 &
281 ⦃G, L⦄ ⊢ W1 ➡[h] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ➡[n, h] T2 &
282 U1 = ⓓ{p}W1.T1 & U2 = ⓓ{p}W2.ⓐV2.T2.
283 #n #h #G #L #V1 #U1 #U2 * #c #Hc #H elim (cpg_inv_appl1 … H) -H *
284 [ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
285 elim (isrt_inv_plus … Hc) -Hc #nV #nT #HcV #HcT #H destruct
286 elim (isrt_inv_shift … HcV) -HcV #HcV #H destruct
287 /4 width=5 by or3_intro0, ex3_2_intro, ex2_intro/
288 | #cV #cW #cT #p #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 #HT12 #H1 #H2 #H3 destruct
289 lapply (isrt_inv_plus_O_dx … Hc ?) -Hc // #Hc
290 elim (isrt_inv_plus … Hc) -Hc #n0 #nT #Hc #HcT #H destruct
291 elim (isrt_inv_plus … Hc) -Hc #nV #nW #HcV #HcW #H destruct
292 elim (isrt_inv_shift … HcV) -HcV #HcV #H destruct
293 elim (isrt_inv_shift … HcW) -HcW #HcW #H destruct
294 /4 width=11 by or3_intro1, ex5_6_intro, ex2_intro/
295 | #cV #cW #cT #p #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 #HW12 #HT12 #H1 #H2 #H3 destruct
296 lapply (isrt_inv_plus_O_dx … Hc ?) -Hc // #Hc
297 elim (isrt_inv_plus … Hc) -Hc #n0 #nT #Hc #HcT #H destruct
298 elim (isrt_inv_plus … Hc) -Hc #nV #nW #HcV #HcW #H destruct
299 elim (isrt_inv_shift … HcV) -HcV #HcV #H destruct
300 elim (isrt_inv_shift … HcW) -HcW #HcW #H destruct
301 /4 width=13 by or3_intro2, ex6_7_intro, ex2_intro/
305 lemma cpm_inv_cast1: ∀n,h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓝV1.U1 ➡[n, h] U2 →
306 ∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ U1 ➡[n,h] T2 &
308 | ⦃G, L⦄ ⊢ U1 ➡[n, h] U2
309 | ∃∃m. ⦃G, L⦄ ⊢ V1 ➡[m, h] U2 & n = ⫯m.
310 #n #h #G #L #V1 #U1 #U2 * #c #Hc #H elim (cpg_inv_cast1 … H) -H *
311 [ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
312 elim (isrt_inv_plus … Hc) -Hc #nV #nT #HcV #HcT #H destruct
313 elim (isrt_inv_shift … HcV) -HcV #HcV #H destruct
314 /4 width=5 by or3_intro0, ex3_2_intro, ex2_intro/
315 | #cU #U12 #H destruct
316 /4 width=3 by isrt_inv_plus_O_dx, or3_intro1, ex2_intro/
317 | #cU #H12 #H destruct
318 elim (isrt_inv_plus_SO_dx … Hc) -Hc // #m #Hc #H destruct
319 /4 width=3 by or3_intro2, ex2_intro/
323 (* Basic forward lemmas *****************************************************)
325 (* Basic_2A1: includes: cpr_fwd_bind1_minus *)
326 lemma cpm_fwd_bind1_minus: ∀n,h,I,G,L,V1,T1,T. ⦃G, L⦄ ⊢ -ⓑ{I}V1.T1 ➡[n, h] T → ∀p.
327 ∃∃V2,T2. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ➡[n, h] ⓑ{p,I}V2.T2 &
329 #n #h #I #G #L #V1 #T1 #T * #c #Hc #H #p elim (cpg_fwd_bind1_minus … H p) -H
330 /3 width=4 by ex2_2_intro, ex2_intro/