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Proof step 11 from proof junkrefs-put-nopathex-equiv (previous step)

st[r1 -- mkfs(class, ty1, fieldvar) '] = refval(r2), st[r1 -- _type] .type ≤ ty, is_obj(str, r1, st), is_valid_ref(str, r0, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), junkrefs(str, r2 ' + refs, ty1, st), path∃(str, r2, r0, st), ∀ str0, r, st0, sk0, ty0, val0. ¬ path∃(str0, r2, r, st0) ∧ is_valid_ref(str0, r, st0) ∧ sk0 ≠ _type → (junkrefs(str0, r2 ' + refs, ty0, st0[r -- sk0, val0]) ↔ junkrefs(str0, r2 ' + refs, ty0, st0)) ⊦ r1 = jvmref, sk = _type, r1 = r0, r2 = jvmref, junkrefs(str, r2 ' + refs, ty1, st[r0 -- sk, val]), st[r2 -- _type] .type ≤ ty1

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], ty1, refs, r2, str] ,F ,junkrefs , ,junkrefs-is-junk ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]])], [EXTRATERMS : (st[r0 -- sk, val], ty1, refs, r2, str)]]