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Proof step 53 from proof ex-validrefs-fits-stronger (previous step)

refs0 .first = st[r -- i '] .refval, is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, refs0, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ st, ty, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, ty, st) → (∃ sks. fits(r, sks, st) ∧ # sks = # refs ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st[r -- firstn(n, sks)] .refval = (r ' + refs)[n]))) ⊦ refs0 = [], r = jvmref, ∃ sks. fits(r, sks, st) ∧ # sks = # refs0 ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st[r -- firstn(n, sks)] .refval = (r ' + refs0)[n])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs0, r0, refs1] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs0, r0, refs1)]]