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Proof step 22 from proof junkrefs-put-refval (previous step)

junkrefs(str, st[r1 -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, ty0, st), is_obj(str, r1, st), junkrefs(str, r3 ' + refs, ty0, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r3)]), is_obj(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r3)]), st[r1 -- _type] .type ≤ ty, is_obj(r1, st), st[r3 -- _type] .type ≤ ty0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), is_referencevalue(st[r1 -- mkfs(class, ty0, fieldvar) ']), ∀ 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)]) ⊦ r1 = jvmref, r3 = jvmref, _type = mkfs(class, ty0, fieldvar) ', r3 = st[r1 -- mkfs(class, ty0, fieldvar) '] .refval, junkref(str, r3, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
st[r1 -- mkfs(class, ty0, fieldvar) '] = refval(r0), junkrefs(str, r0 ' + refs, ty0, st), is_obj(str, r1, st), junkrefs(str, r3 ' + refs, ty0, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r3)]), is_obj(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r3)]), st[r1 -- _type] .type ≤ ty, is_obj(r1, st), st[r3 -- _type] .type ≤ ty0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), is_referencevalue(st[r1 -- mkfs(class, ty0, fieldvar) ']), ∀ 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)]) ⊦ r1 = jvmref, r3 = jvmref, _type = mkfs(class, ty0, fieldvar) ', r3 = r0, junkref(str, r3, st)

Rule argument

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

Additional information

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