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Proof step 9 from proof junkrefs-put-null (previous step)

r0 -- _type ≠ r -- mkfs(class, ty0, fieldvar) ', 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_obj(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 ≠ r ∨ _type ≠ mkfs(class, ty0, fieldvar) ' ⊦ r0 = jvmref, junkrefs(str, r0 ' + acc, ty, st), is_obj(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]) ∧ st[r0 -- _type] .type ≤ ty

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
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_obj(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 ≠ r ∨ _type ≠ mkfs(class, ty0, fieldvar) ' ⊦ r0 = jvmref, junkrefs(str, r0 ' + acc, ty, st), is_obj(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]