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

(acc + r0 ') .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, acc + r0 ' + refs, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ str, refs0, st, ty. ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∧ refs0 ≠ [] → ¬ validrefs(str, acc + refs0, ty, st) ⊦ r = jvmref, validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
acc + r0 ' = r1 + refs1 ∧ acc + r0 ' ≠ [], r1 = 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, acc + r0 ' + refs, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ str, refs0, st, ty. ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∧ refs0 ≠ [] → ¬ validrefs(str, acc + refs0, ty, st) ⊦ r = jvmref, validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [acc + r0 ', r1, refs1] ,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 + r0 ', r1, refs1)]]