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Proof step 11 from proof validrefs-levelsubset (previous step)

is_obj(str0, r, st), st[r -- _type] .type ≤ ty0, level⊆(str, str0), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty, fieldvar) ']), validrefs(str, st[r -- mkfs(class, ty, fieldvar) '] .refval ' + refs, ty, st), ∀ str1, ty1, st0, str2. validrefs(str1, st[r -- mkfs(class, ty, fieldvar) '] .refval ' + refs, ty1, st0) ∧ level⊆(str1, str2) → validrefs(str2, st[r -- mkfs(class, ty, fieldvar) '] .refval ' + refs, ty1, st0) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- mkfs(class, ty, fieldvar) '] .refval = st[r -- fs '] .refval ∧ validrefs(str0, st[r -- mkfs(class, ty, fieldvar) '] .refval ' + refs, fs .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), is_obj(str0, r, st), st[r -- _type] .type ≤ ty0, level⊆(str, str0), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty, fieldvar) ']), validrefs(str, r0 ' + refs, ty, st), ∀ str1, ty1, st0, str2. validrefs(str1, r0 ' + refs, ty1, st0) ∧ level⊆(str1, str2) → validrefs(str2, r0 ' + refs, ty1, st0) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ validrefs(str0, r0 ' + refs, fs .type, st)

Rule argument

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

Additional information

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