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Proof step 26 from proof junkrefs-put-refval-01 (previous step)

st[r0 -- _type] .type ≤ ty0, is_obj(str, r1, st), is_obj(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), st[r1 -- _type] .type ≤ ty, mkfs(class0, ty2, fieldvar0) ' ∈ instfields(st[r1 -- _type] .type .class), is_referencevalue(st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- mkfs(class0, ty2, fieldvar0) ']), junkrefs (str, (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- mkfs(class0, ty2, fieldvar0) ']) .refval ' + refs, ty2, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), ∀ str0, ty1, st0, r, fs0, r2. ¬ junkrefs(str0, (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- mkfs(class0, ty2, fieldvar0) ']) .refval ' + refs, ty1, st0) ∧ ¬ junkref(str0, r, st0) ∧ st0[r -- _type] .type ≤ fs0 .type ∧ r ≠ jvmref ∧ fs0 .type ≠ void_type ∧ fs0 ' ≠ _length → ¬ junkrefs (str0, (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- mkfs(class0, ty2, fieldvar0) ']) .refval ' + refs, ty1, st0[r2 -- fs0 ', refval(r)]) ⊦ r0 = jvmref, ty0 = void_type, mkfs(class, ty0, fieldvar) ' = _length, r1 = jvmref, junkref(str, r0, st), ∃ fs0. fs0 ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs0 ']) ∧ (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- mkfs(class0, ty2, fieldvar0) ']) .refval = st[r1 -- fs0 '] .refval ∧ junkrefs(str, (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- mkfs(class0, ty2, fieldvar0) ']) .refval ' + refs, fs0 .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 25:
(st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- mkfs(class0, ty2, fieldvar0) ']) = refval(r3), st[r0 -- _type] .type ≤ ty0, is_obj(str, r1, st), is_obj(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), st[r1 -- _type] .type ≤ ty, mkfs(class0, ty2, fieldvar0) ' ∈ instfields(st[r1 -- _type] .type .class), is_referencevalue(st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- mkfs(class0, ty2, fieldvar0) ']), junkrefs(str, r3 ' + refs, ty2, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), ∀ str0, ty1, st0, r, fs0, r2. ¬ junkrefs(str0, r3 ' + refs, ty1, st0) ∧ ¬ junkref(str0, r, st0) ∧ st0[r -- _type] .type ≤ fs0 .type ∧ r ≠ jvmref ∧ fs0 .type ≠ void_type ∧ fs0 ' ≠ _length → ¬ junkrefs(str0, r3 ' + refs, ty1, st0[r2 -- fs0 ', refval(r)]) ⊦ r0 = jvmref, ty0 = void_type, mkfs(class, ty0, fieldvar) ' = _length, r1 = jvmref, junkref(str, r0, st), ∃ fs0. fs0 ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs0 ']) ∧ r3 = st[r1 -- fs0 '] .refval ∧ junkrefs(str, r3 ' + refs, fs0 .type, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)] [r1 -- mkfs(class0, ty2, fieldvar0) ' ], r3] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)] [r1 -- mkfs(class0, ty2, fieldvar0) ' ], r3)]]