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Proof step 25 from proof validrefs-not-contains (previous step)

validrefs(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval ', 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) ⊦ r = jvmref, r = st[r -- mkfs(class, ty0, fieldvar) '] .refval, st[r -- mkfs(class, ty0, fieldvar) '] .refval = jvmref, contains(str, st[r -- _type] .type, st[st[r -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 24:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), validrefs(str, r0 ', 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) ⊦ r = jvmref, r = r0, r0 = jvmref, contains(str, st[r -- _type] .type, st[r0 -- _type] .type)

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)]]