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Proof step 56 from proof junkrefs-put-nopathexplus-equiv (previous step)

is_obj(str, r, st[r0 -- sk, val]) ∧ (st[r0 -- sk, val][r -- _type]) .type ≤ ty, st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), junkrefs(str, r1 ' + refs1, ty0, st), st[r -- _type] .type ≤ ty, is_obj(str, r, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), ∀ val, sk, r0, st0, ty, r2, str, refs. # refs < # (r1 + refs1) → (junkrefs(str, r2 ' + refs, ty, st0) → junkrefs(str, r2 ' + refs, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ r = r0, r = jvmref, sk = _type, r1 ' + refs1 ≠ [] ∧ (∃ fs. fs ' ∈ instfields((st[r0 -- sk, val][r -- _type]) .type .class) ∧ is_referencevalue(st[r0 -- sk, val][r -- fs ']) ∧ (r1 ' + refs1) .first = (st[r0 -- sk, val][r -- fs ']) .refval ∧ junkrefs(str, r1 ' + refs1, fs .type, st[r0 -- sk, val])), path∃+(str, r, r0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), junkrefs(str, r1 ' + refs1, ty0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), st[r -- _type] .type ≤ ty, ∀ val, sk, r0, st0, ty, r2, str, refs. # refs < # (r1 + refs1) → (junkrefs(str, r2 ' + refs, ty, st0) → junkrefs(str, r2 ' + refs, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ r = r0, r = jvmref, sk = _type, path∃+(str, r, r0, st), ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r1 = st[r -- fs '] .refval ∧ junkrefs(str, st[r -- fs '] .refval ' + refs1, fs .type, st[r0 -- sk, val])

Rule argument

[emptyarg]

Additional information

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