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Proof step 86 from proof pathex-put-nopathex (previous step)

is_array(str, r, st[r0 -- sk, val]), validrefs(str, r ' + refs0, st[r -- _type] .type, st[r0 -- sk, val]), ∀ val, sk, r0, st, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, st[r -- _type] .type, st[r0 -- sk, val]) → sk = _type ∨ path∃(str, r, r0, st) ∨ junkref(str, r, st) ∨ path∃(str, r, (r ' + refs) .last, st)) ⊦ sk = _type, r = jvmref, path∃(str, r, (r ' + refs0) .last, st), junkref(str, r, st), path∃(str, r, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 85:
is_array(str, r, st[r0 -- sk, val]) ∧ (st[r0 -- sk, val][r -- _type]) .type ≤ st[r -- _type] .type, is_array(str, r, st[r0 -- sk, val]), refs0 = [] ∨ (∃ i. 0 ≤ i ∧ i < (st[r0 -- sk, val][r -- _length]) .intval ∧ is_referencevalue(st[r0 -- sk, val][r -- i ']) ∧ refs0 .first = (st[r0 -- sk, val][r -- i ']) .refval ∧ validrefs(str, refs0, (st[r0 -- sk, val][r -- _type]) .type .type, st[r0 -- sk, val])), ∀ val, sk, r0, st, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, st[r -- _type] .type, st[r0 -- sk, val]) → sk = _type ∨ path∃(str, r, r0, st) ∨ junkref(str, r, st) ∨ path∃(str, r, (r ' + refs) .last, st)) ⊦ sk = _type, r = jvmref, path∃(str, r, (r ' + refs0) .last, st), junkref(str, r, st), path∃(str, r, r0, st)

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st[r0 -- sk, val], st[r -- _type] .type, refs0, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ ty ≤ ty])], [EXTRATERMS : (st[r0 -- sk, val], st[r -- _type] .type, refs0, r, str)]]