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Proof step 16 from proof junkrefs-put-norefval-equiv (previous step)

st[r -- mkfs(class1, ty3, fieldvar1) '] = refval(r2), junkrefs(str, r2 ' + refs, ty3, st), mkfs(class1, ty3, fieldvar1) ' ∈ instfields(st[r -- _type] .type .class), r1 ∈ st, okval(val, ty0), r1 -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(st[r1 -- mkfs(class, ty0, fieldvar) '], ty0), is_obj(str, r, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), is_obj(str, r, st), st[r -- _type] .type ≤ ty, ∀ st0, r0, class0, ty1, fieldvar0, val0, str0, ty2. okval(st0[r0 -- mkfs(class0, ty1, fieldvar0) '], ty1) ∧ r0 -- mkfs(class0, ty1, fieldvar0) ' ∈ st0 ∧ okval(val0, ty1) ∧ r0 ∈ st0 ∧ junkrefs(str0, r2 ' + refs, ty2, st0) → mkfs(class0, ty1, fieldvar0) ' = _length ∨ ty1 = void_type ∨ is_referencevalue(val0) ∨ junkrefs(str0, r2 ' + refs, ty2, st0[r0 -- mkfs(class0, ty1, fieldvar0) ', val0]) ⊦ r = jvmref, ty0 = void_type, mkfs(class, ty0, fieldvar) ' = _length, is_referencevalue(val), is_referencevalue(st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- mkfs(class1, ty3, fieldvar1) ']) ∧ r2 = (st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- mkfs(class1, ty3, fieldvar1) ']) .refval ∧ junkrefs (str, (st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- mkfs(class1, ty3, fieldvar1) ']) .refval ' + refs, ty3, st[r1 -- mkfs(class, ty0, fieldvar) ', val])

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 15:
st[r -- mkfs(class1, ty3, fieldvar1) '] = refval(r2), junkrefs(str, r2 ' + refs, ty3, st), mkfs(class1, ty3, fieldvar1) ' ∈ instfields(st[r -- _type] .type .class), r1 ∈ st, okval(val, ty0), r1 -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(st[r1 -- mkfs(class, ty0, fieldvar) '], ty0), is_obj(str, r, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), is_obj(str, r, st), st[r -- _type] .type ≤ ty, ∀ st0, r0, class0, ty1, fieldvar0, val0, str0, ty2. okval(st0[r0 -- mkfs(class0, ty1, fieldvar0) '], ty1) ∧ r0 -- mkfs(class0, ty1, fieldvar0) ' ∈ st0 ∧ okval(val0, ty1) ∧ r0 ∈ st0 ∧ junkrefs(str0, r2 ' + refs, ty2, st0) → mkfs(class0, ty1, fieldvar0) ' = _length ∨ ty1 = void_type ∨ is_referencevalue(val0) ∨ junkrefs(str0, r2 ' + refs, ty2, st0[r0 -- mkfs(class0, ty1, fieldvar0) ', val0]) ⊦ r -- mkfs(class1, ty3, fieldvar1) ' = r1 -- mkfs(class, ty0, fieldvar) ', r = jvmref, ty0 = void_type, mkfs(class, ty0, fieldvar) ' = _length, is_referencevalue(val), is_referencevalue(st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- mkfs(class1, ty3, fieldvar1) ']) ∧ r2 = (st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- mkfs(class1, ty3, fieldvar1) ']) .refval ∧ junkrefs (str, (st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- mkfs(class1, ty3, fieldvar1) ']) .refval ' + refs, ty3, st[r1 -- mkfs(class, ty0, fieldvar) ', val])

Rule argument

[fma-arg: r -- mkfs(class1, ty3, fieldvar1) ' = r1 -- mkfs(class, ty0, fieldvar) ' ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (st[rk, val][rk]) = val], [CSIMPSEQ : ⊦ okval(refval(r), ty) ↔ ty = void_type ∨ is_reftype(ty)], [CSIMPSEQ : ⊦ is_reftype(ty) → ( okval(val, ty) ↔ is_referencevalue(val))])], [EXTRAFMAS : ( r -- mkfs(class1, ty3, fieldvar1) ' = r1 -- mkfs(class, ty0, fieldvar) ')]]