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

st[r1 -- _type] .type ≤ ty, is_valid_ref(str, r1, st), junkrefs(str, r1 ' + acc, ty, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), st[r0 -- _type] .type ≤ ty0, is_obj(r1, st), ∀ str, ty, st, r0, r, fs. ¬ junkrefs(str, acc, ty, st) ∧ ¬ junkref(str, r0, st) ∧ is_obj(r, st) ∧ st[r0 -- _type] .type ≤ fs .type ∧ r0 ≠ jvmref ∧ fs ' ∈ instfields(st[r -- _type] .type .class) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(r0)]) ⊦ r1 -- _type = r1 -- mkfs(class, ty0, fieldvar) ', r0 = jvmref, r1 = jvmref, junkrefs(str, r1 ' + acc, ty, st), junkref(str, r0, st), is_obj(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]) ∧ (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type ≤ ty

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
st[r1 -- _type] .type ≤ ty, is_valid_ref(str, r1, st), junkrefs(str, r1 ' + acc, ty, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), st[r0 -- _type] .type ≤ ty0, is_obj(r1, st), ∀ str, ty, st, r0, r, fs. ¬ junkrefs(str, acc, ty, st) ∧ ¬ junkref(str, r0, st) ∧ is_obj(r, st) ∧ st[r0 -- _type] .type ≤ fs .type ∧ r0 ≠ jvmref ∧ fs ' ∈ instfields(st[r -- _type] .type .class) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(r0)]) ⊦ r0 = jvmref, r1 = jvmref, _type = mkfs(class, ty0, fieldvar) ', junkrefs(str, r1 ' + acc, ty, st), junkref(str, r0, st), is_obj(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)])

Rule argument

[emptyarg]

Additional information

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