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Proof step 21 from proof junkrefs-put-nopathex-equiv (previous step)

st[r1 -- mkfs(class, ty1, fieldvar) '] = refval(r2), junkrefs(str, r2 ' + refs, ty1, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), is_valid_ref(str, r0, st), st[r1 -- _type] .type ≤ ty, is_obj(str, r1, 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)) ⊦ sk = _type, r1 = jvmref, r0 = r1, junkrefs(str, r1 ' + r2 ' + refs, ty, st[r0 -- sk, val]), path∃(str, r1, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ junkrefs(str, refs, fs .type, st)))
Proof step 20:
is_obj(str, r1, st[r0 -- sk, val]) ∧ (st[r0 -- sk, val][r1 -- _type]) .type ≤ ty, st[r1 -- mkfs(class, ty1, fieldvar) '] = refval(r2), junkrefs(str, r2 ' + refs, ty1, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), is_valid_ref(str, r0, st), st[r1 -- _type] .type ≤ ty, is_obj(str, r1, 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)) ⊦ sk = _type, r1 = jvmref, r0 = r1, r2 ' + refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields((st[r0 -- sk, val][r1 -- _type]) .type .class) ∧ is_referencevalue(st[r0 -- sk, val][r1 -- fs ']) ∧ (r2 ' + refs) .first = (st[r0 -- sk, val][r1 -- fs ']) .refval ∧ junkrefs(str, r2 ' + refs, fs .type, st[r0 -- sk, val])), path∃(str, r1, r0, st)

Rule argument

[speclemmaarg: , is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ junkrefs(str, refs, fs .type, st))) ,[st, ty, refs, r, str] → [st[r0 -- sk, val], ty, r2 ' + refs, r1, str] ,F ,junkrefs , ,junkrefs-class ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( is_obj (str, r0, st[r -- sk, val]) ↔ is_obj(str, r0, st))], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]])], [EXTRATERMS : (st[r0 -- sk, val], ty, r2 ' + refs, r1, str)]]