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Proof step 35 from proof junkrefs-put-nopathexplus-equiv (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), validrefs(str, r1 ' + refs2, mkclasstype(`java.lang.Object' .class), st), step∃(str, (r1 ' + refs2) .last, r0, st), junkrefs(str, r1 ' + refs1, ty0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), st[r -- _type] .type ≤ ty, validrefs(str, r1 ' + refs2, st[r1 -- _type] .type, 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)) ⊦ r1 = r0, r = r0, r = jvmref, sk = _type, junkrefs(str, r1 ' + refs1, ty0, st[r0 -- sk, val]), validrefs(str, r1 ' + refs2, ty0, st), st[r1 -- _type] .type ≤ ty0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → junkrefs(str, r ' + refs, ty, st) ,[st, ty, refs, r, str] → [st[r0 -- sk, val], ty0, refs1, r1, str] ,F ,junkrefs , ,junkrefs-is-junk ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_valid_ref (str, r0, st[r -- sk, val]) ↔ is_valid_ref(str, r0, st))], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ ¬ junkrefs (str, jvmref ' + refs, ty, st)])], [EXTRATERMS : (st[r0 -- sk, val], ty0, refs1, r1, str)]]