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Proof step 33 from proof validrefs-put-last (previous step)

acc + r0 ' = st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, validrefs(str, acc + r0 ', ty0, st[r0 -- sk, val]), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, is_obj(str, r, st), ∀ str, r0, ty, st, sk, val. ¬ validrefs(str, acc + r0 ', ty, st) ∧ ¬ junkref(str, acc .first, st) ∧ acc ≠ [] ∧ ¬ r0 ∈ acc ∧ sk ≠ _type → ¬ validrefs(str, acc + r0 ', ty, st[r0 -- sk, val]) ⊦ r = jvmref, r0 = r, sk = _type, validrefs(str, (r ' + acc) + r0 ', ty, st), junkref(str, r, st), r0 ∈ acc, r0 ≠ st[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ ¬ r0 ∈ refs, ¬ st[r -- mkfs(class, ty0, fieldvar) '] .refval ∈ acc ∧ st[r -- mkfs(class, ty0, fieldvar) '] .refval ≠ r0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), acc + r0 ' = r1 ' + refs, validrefs(str, acc + r0 ', ty0, st[r0 -- sk, val]), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, is_obj(str, r, st), ∀ str, r0, ty, st, sk, val. ¬ validrefs(str, acc + r0 ', ty, st) ∧ ¬ junkref(str, acc .first, st) ∧ acc ≠ [] ∧ ¬ r0 ∈ acc ∧ sk ≠ _type → ¬ validrefs(str, acc + r0 ', ty, st[r0 -- sk, val]) ⊦ r = jvmref, r0 = r, sk = _type, validrefs(str, (r ' + acc) + r0 ', ty, st), junkref(str, r, st), r0 ∈ acc, r0 ≠ r1 ∧ ¬ r0 ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r0

Rule argument

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

Additional information

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