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Proof step 9 from proof validrefs-superclass (previous step)

is_obj(str, r, st), ty ≤ ty0, st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty0, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']), validrefs(str, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty1, st), ∀ ty2, ty3, str0, st0. ty2 ≤ ty3 ∧ validrefs(str0, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty2, st0) → validrefs(str0, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty3, st0) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- mkfs(class, ty1, fieldvar) '] .refval = st[r -- fs '] .refval ∧ validrefs(str, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, fs .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), is_obj(str, r, st), ty ≤ ty0, st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty0, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']), validrefs(str, r0 ' + refs, ty1, st), ∀ ty2, ty3, str0, st0. ty2 ≤ ty3 ∧ validrefs(str0, r0 ' + refs, ty2, st0) → validrefs(str0, r0 ' + refs, ty3, st0) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ validrefs(str, r0 ' + refs, fs .type, st)

Rule argument

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

Additional information

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