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Proof step 58 from proof junkrefs-put-refval (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 57:
(st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- mkfs(class0, ty2, fieldvar0) ']) = refval(r3), is_referencevalue(st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- mkfs(class0, ty2, fieldvar0) ']), mkfs(class0, ty2, fieldvar0) ' ∈ instfields((st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type .class), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), st[r0 -- _type] .type ≤ ty0, is_obj(r1, st), (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type ≤ ty, is_obj(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), st[r1 -- _type] .type ≤ ty, is_valid_ref(str, r1, st), junkrefs(str, r3 ' + refs, ty2, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), ∀ str0, ty1, st0, r, r2, fs0. ¬ junkrefs(str0, r3 ' + refs, ty1, st0) ∧ ¬ junkref(str0, r, st0) ∧ is_obj(r2, st0) ∧ st0[r -- _type] .type ≤ fs0 .type ∧ r ≠ jvmref ∧ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ junkrefs(str0, r3 ' + refs, ty1, st0[r2 -- fs0 ', refval(r)]) ⊦ r0 = jvmref, r1 = jvmref, junkref(str, r0, st), junkrefs(str, r1 ' + r3 ' + refs, ty, 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)]]