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Proof step 37 from proof junkrefs-put-null (previous step)

st[r0 -- _type] .type ≤ ty, is_obj(r, st), is_reftype(ty0), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), junkrefs(str, r0 ' + acc, ty, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), is_array(str, r0, st), ∀ str, ty, st, r, fs. ¬ junkrefs(str, acc, ty, st) ∧ is_obj(r, st) ∧ is_reftype(fs .type) ∧ fs ' ∈ instfields(st[r -- _type] .type .class) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(jvmref)]) ⊦ r0 = jvmref, junkrefs(str, r0 ' + acc, ty, st), is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]) ∧ (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type ≤ ty

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

[fma-arg: r0 -- _type = r -- mkfs(class, ty0, fieldvar) ']

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkfs (`java.lang.Object' .class, void_type, `type' .field) ' = _type], [CSIMPFORWARD : ⊦ _type = mkfs(class1, ty, fieldvar) ' → class1 = `java.lang.Object' .class ∧ ty = void_type ∧ fieldvar = `type' .field], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ is_obj(r, st) → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]])], [EXTRAFMAS : (r0 -- _type = r -- mkfs(class, ty0, fieldvar) ')]]