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Proof step 36 from proof hasSharing-pathex (previous step)

st[r -- i '] = refval(r1), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), hasSharing(r0, st), i < st[r -- _length] .intval, validrefs(str, (r1 ' + refs0) + r0 ', st[r -- _type] .type .type, st), ∀ st, r, str, refs. # refs < # (r1 ' + refs0 + r0 ') → (validrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ hasSharing(refs .last, st) → refs = [] ∨ hasSharing(r, st)) ⊦ r = jvmref, hasSharing(r, st), validrefs(str, r1 ' + refs0 + r0 ', st[r1 -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , validrefs(str, refs, ty, st) ∧ refs ≠ [] ∧ refs .first ≠ jvmref ∧ r = refs .first → validrefs(str, refs, st[r -- _type] .type, st) ,[str, refs, ty, st, r] → [str, r1 ' + refs0 + r0 ', st[r -- _type] .type .type, st, r1] ,F ,cyclic , ,validrefs-sametype-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ validrefs (str, jvmref ' + refs, ty, st) ↔ refs = []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (str, r1 ' + refs0 + r0 ', st[r -- _type] .type .type, st, r1)]]