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Proof step 16 from proof validrefs-contains-null (previous step)

acc + jvmref ' = st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, validrefs(str, acc + jvmref ' + refs0, ty0, st), 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, refs0, ty, st. validrefs(str, acc + jvmref ' + refs0, ty, st) → validrefs(str, acc + jvmref ', ty, st) ∧ refs0 = [] ⊦ r = jvmref, validrefs(str, (r ' + acc) + jvmref ', ty, st) ∧ refs0 = [], jvmref ≠ st[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ ¬ jvmref ∈ refs, ¬ st[r -- mkfs(class, ty0, fieldvar) '] .refval ∈ acc ∧ st[r -- mkfs(class, ty0, fieldvar) '] .refval ≠ jvmref

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), acc + jvmref ' = r0 ' + refs, validrefs(str, acc + jvmref ' + refs0, ty0, st), 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, refs0, ty, st. validrefs(str, acc + jvmref ' + refs0, ty, st) → validrefs(str, acc + jvmref ', ty, st) ∧ refs0 = [] ⊦ r = jvmref, validrefs(str, (r ' + acc) + jvmref ', ty, st) ∧ refs0 = [], jvmref ≠ r0 ∧ ¬ jvmref ∈ refs, ¬ r0 ∈ acc ∧ r0 ≠ jvmref

Rule argument

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

Additional information

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