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Proof step 9 from proof validrefs-set-null (previous step)

is_referencevalue(st[r -- mkfs(class0, ty1, fieldvar0) ']), mkfs(class0, ty1, fieldvar0) ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, is_reftype(ty0), is_obj(str, r, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, st[r -- mkfs(class0, ty1, fieldvar0) '] .refval ' + refs, ty1, st) ⊦ r = jvmref, _type = mkfs(class, ty0, fieldvar) ', validrefs(str, r ' + jvmref ', ty, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), is_obj(str, r, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
st[r -- mkfs(class0, ty1, fieldvar0) '] = refval(r0), is_referencevalue(st[r -- mkfs(class0, ty1, fieldvar0) ']), mkfs(class0, ty1, fieldvar0) ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty, is_reftype(ty0), is_obj(str, r, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r0 ' + refs, ty1, st) ⊦ r = jvmref, _type = mkfs(class, ty0, fieldvar) ', validrefs(str, r ' + jvmref ', ty, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), is_obj(str, r, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)])

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r -- mkfs(class0, ty1, fieldvar0) '], r0] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- mkfs(class0, ty1, fieldvar0) '], r0)]]