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Proof step 29 from proof junkrefs-put-null (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 28:
(st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- mkfs(class0, ty2, fieldvar0) ']) = refval(r2), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- mkfs(class0, ty2, fieldvar0) ']), mkfs(class0, ty2, fieldvar0) ' ∈ instfields((st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type .class), is_obj(str, r0, st), (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type ≤ ty, is_obj(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), st[r0 -- _type] .type ≤ ty, is_obj(r, st), is_reftype(ty0), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), junkrefs(str, r2 ' + refs, ty2, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), ∀ str0, ty1, st0, r1, fs0. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ is_obj(r1, st0) ∧ is_reftype(fs0 .type) ∧ fs0 ' ∈ instfields(st0[r1 -- _type] .type .class) → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r1 -- fs0 ', refval(jvmref)]) ⊦ r0 = jvmref, junkrefs(str, r0 ' + r2 ' + refs, ty, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)] [r0 -- mkfs(class0, ty2, fieldvar0) ' ], r2] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)] [r0 -- mkfs(class0, ty2, fieldvar0) ' ], r2)]]