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Proof step 24 from proof validrefs-superclass (previous step)

acc .first = st[r -- i '] .refval, is_array(str, r, st), ty ≤ ty0, st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty0, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, acc, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ ty, ty0, str, st. ty ≤ ty0 ∧ validrefs(str, acc, ty, st) → validrefs(str, acc, ty0, st) ⊦ r = jvmref, acc = [], ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ acc .first = st[r -- i0 '] .refval

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
acc = r0 + refs, r0 = st[r -- i '] .refval, is_array(str, r, st), ty ≤ ty0, st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty0, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, acc, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ ty, ty0, str, st. ty ≤ ty0 ∧ validrefs(str, acc, ty, st) → validrefs(str, acc, ty0, st) ⊦ r = jvmref, acc = [], ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r0 = st[r -- i0 '] .refval

Rule argument

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

Additional information

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