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Proof step 113 from proof validrefs-lastelem (previous step)

(acc + r ') .first = st[r0 -- i '] .refval, is_array(str, r0, st), validrefs(str, r0 ' + acc, ty, st), st[r0 -- _type] .type ≤ ty, i < st[r0 -- _length] .intval, is_referencevalue(st[r0 -- i ']), validrefs(str, acc + r ', st[r0 -- _type] .type .type, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, ∀ str, ty, st, r. validrefs(str, acc, ty, st) ∧ validrefs(str, acc + r ', ty, st) → acc = [] ∨ has_reffield(acc .last, st) ⊦ r0 = jvmref, has_reffield((r0 ' + acc) .last, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 112:
acc + r ' = r1 + refs ∧ acc + r ' ≠ [], r1 = st[r0 -- i '] .refval, is_array(str, r0, st), validrefs(str, r0 ' + acc, ty, st), st[r0 -- _type] .type ≤ ty, i < st[r0 -- _length] .intval, is_referencevalue(st[r0 -- i ']), validrefs(str, acc + r ', st[r0 -- _type] .type .type, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, ∀ str, ty, st, r. validrefs(str, acc, ty, st) ∧ validrefs(str, acc + r ', ty, st) → acc = [] ∨ has_reffield(acc .last, st) ⊦ r0 = jvmref, has_reffield((r0 ' + acc) .last, st)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [acc + r ', r1, refs] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (acc + r ', r1, refs)]]