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Proof step 78 from proof junkrefs-put-nopathexplus-equiv (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 70:
⊦ validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty
Proof step 77:
st[r -- i '] = refval(r0), junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, 0 < st[r -- _length] .intval, 0 ≤ i, is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ val, sk, r, st0, ty, r2, str, refs. # refs < # (r0 + refs1) → (junkrefs(str, r2 ' + refs, ty, st0) → junkrefs(str, r2 ' + refs, ty, st0[r -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r, st0)) ⊦ r = r0, sk = _type, r = jvmref, junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st[r0 -- sk, val]), (r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ mkclasstype(`java.lang.Object' .class)) ∧ step∃(str, r, r0, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, mkclasstype(`java.lang.Object' .class), r, str)]]