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Proof step 47 from proof hasSharing-dd-help (previous step)

# refs1 = # refs3 + # refs2, # sks0 = 2 + # refs + # refs1, # refs4 = # refs, st[r -- firstn(1 + # refs, sks0)] .refval = (refs4 + refs3)[# refs], fits(r, sks0, st), validrefs(str, (r ' + refs4 + refs3) + r2 ' + refs2 + r0 ', st[r -- _type] .type, st), validrefs(str, (r ' + refs) + (refs4 + refs3)[# refs] ' + refs1 + r0 ', st[r -- _type] .type, st) ⊦ refs3 = [], refs4 + refs3 = [], r0 = jvmref, (refs4 + refs3)[# refs] = r0, r2 = (refs4 + refs3)[# refs], hasSharing(r, st), path∃(str, (refs4 + refs3)[# refs], r2, st), path∃(str, r2, (refs4 + refs3)[# refs], st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ ¬ n < # refs → (refs + refs0)[n] = refs0[n - # refs]
Proof step 46:
¬ # refs < # refs4, # refs1 = # refs3 + # refs2, # sks0 = 2 + # refs + # refs1, # refs4 = # refs, st[r -- firstn(1 + # refs, sks0)] .refval = refs3[# refs - # refs4], fits(r, sks0, st), validrefs(str, (r ' + refs4 + refs3) + r2 ' + refs2 + r0 ', st[r -- _type] .type, st), validrefs(str, (r ' + refs) + refs3[# refs - # refs4] ' + refs1 + r0 ', st[r -- _type] .type, st) ⊦ refs3 = [], refs4 + refs3 = [], r0 = jvmref, refs3[# refs - # refs4] = r0, r2 = refs3[# refs - # refs4], hasSharing(r, st), path∃(str, refs3[# refs - # refs4], r2, st), path∃(str, r2, refs3[# refs - # refs4], st)

Rule argument

[speclemmaarg: ,¬ n < # refs → (refs + refs0)[n] = refs0[n - # refs] ,[n, refs0, refs] → [# refs, refs3, refs4] ,F ,list-del ,references ,get-append-grt ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ n < # refs → (refs + refs0)[n] = refs[n]], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPFORWARD : ⊦ m < n ∧ m = n0 → n0 < n], [CSIMPFORWARD : ⊦ m < n ∧ n = n0 → m < n0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPSEQ : ⊦ # refs = 0 ↔ refs = []], [CSIMPSEQ : ⊦ m < n → ¬ n < m])], [EXTRATERMS : (# refs, refs3, refs4)]]