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Proof step 12 from proof junkrefs-put-statfield (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 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 7:
¬ (is_obj(str, r, st[jvmref -- sk, val]) ∧ (st[jvmref -- sk, val][r -- _type]) .type ≤ ty), st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), junkrefs(str, r0 ' + refs, ty1, st), st[r -- _type] .type ≤ ty, is_obj(str, r, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), ∀ str0, ty0, st0, sk0, val0. junkrefs(str0, r0 ' + refs, ty0, st0) → junkrefs(str0, r0 ' + refs, ty0, st0[jvmref -- sk0, val0]) ⊦ r = jvmref, junkrefs(str, r ' + r0 ' + refs, ty, st[jvmref -- sk, val])
Proof step 11:
is_obj(str, r, st[jvmref -- sk, val]) ∧ (st[jvmref -- sk, val][r -- _type]) .type ≤ ty, st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), junkrefs(str, r0 ' + refs, ty1, st), st[r -- _type] .type ≤ ty, is_obj(str, r, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), ∀ str0, ty0, st0, sk0, val0. junkrefs(str0, r0 ' + refs, ty0, st0) → junkrefs(str0, r0 ' + refs, ty0, st0[jvmref -- sk0, val0]) ⊦ r = jvmref, r0 ' + refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields((st[jvmref -- sk, val][r -- _type]) .type .class) ∧ is_referencevalue(st[jvmref -- sk, val][r -- fs ']) ∧ (r0 ' + refs) .first = (st[jvmref -- sk, val][r -- fs ']) .refval ∧ junkrefs(str, r0 ' + refs, fs .type, st[jvmref -- sk, val]))

Rule argument

[crewrite-arg: junkrefs-class , F , [st, ty, refs, r, str] → [st[jvmref -- sk, val], ty, r0 ' + refs, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[jvmref -- sk, val], ty, r0 ' + refs, r, str)]]