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Proof step 12 from proof junkrefs-put-nopathex-equiv (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
st[r1 -- mkfs(class, ty1, fieldvar) '] = refval(r2), st[r1 -- _type] .type ≤ ty, is_obj(str, r1, st), is_valid_ref(str, r0, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), junkrefs(str, r2 ' + refs, ty1, st), path∃(str, r2, r0, 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)) ⊦ r1 = jvmref, sk = _type, r1 = r0, r2 = jvmref, junkrefs(str, r2 ' + refs, ty1, st[r0 -- sk, val]), st[r2 -- _type] .type ≤ ty1

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ junkrefs (str, jvmref ' + refs, ty, st)], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .type = ty], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]