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Proof step 92 from proof junkrefs-put-nopathexplus-equiv (previous step)

st[r -- i '] = refval(r1), st[r -- _type] .type ≤ ty, is_array(str, r, st), 0 ≤ i, 0 < st[r -- _length] .intval, i < st[r -- _length] .intval, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), step∃(str, (r1 ' + refs2) .last, r0, st), validrefs(str, r1 ' + refs2, mkclasstype(`java.lang.Object' .class), st), ∀ val, sk, r0, st0, ty, r2, str, refs0. # refs0 < # (r1 + refs1) → (junkrefs(str, r2 ' + refs0, ty, st0) → junkrefs(str, r2 ' + refs0, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ r = jvmref, sk = _type, r = r0, r1 = r0, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st[r0 -- sk, val]), validrefs(str, r ' + r1 ' + refs2, mkclasstype(`java.lang.Object' .class), st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 82:
⊦ 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 91:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ mkclasstype(`java.lang.Object' .class), st[r -- i '] = refval(r1), st[r -- _type] .type ≤ ty, is_array(str, r, st), 0 ≤ i, 0 < st[r -- _length] .intval, i < st[r -- _length] .intval, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), step∃(str, (r1 ' + refs2) .last, r0, st), validrefs(str, r1 ' + refs2, mkclasstype(`java.lang.Object' .class), st), ∀ val, sk, r0, st0, ty, r2, str, refs0. # refs0 < # (r1 + refs1) → (junkrefs(str, r2 ' + refs0, ty, st0) → junkrefs(str, r2 ' + refs0, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ r = jvmref, sk = _type, r = r0, r1 = r0, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st[r0 -- sk, val]), r1 ' + refs2 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (r1 ' + refs2) .first = st[r -- i '] .refval ∧ validrefs(str, r1 ' + refs2, st[r -- _type] .type .type, st))

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st, mkclasstype(`java.lang.Object' .class), r1 ' + refs2, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ is_array(str, r, st) → ( st[r -- _type] .type ≤ mkclasstype(class) ↔ class = `java.lang.Object' .class)])], [EXTRATERMS : (st, mkclasstype(`java.lang.Object' .class), r1 ' + refs2, r, str)]]