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Proof step 8 from proof validref-class-rec (previous step)

st[r -- _type] .type ≤ ty, is_obj(str, r, st), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), ∀ fs. ¬ fs ' ∈ instfields(st[r -- _type] .type .class) ∨ ¬ is_referencevalue(st[r -- fs ']) ∨ st[r -- fs '] .refval = jvmref ∨ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∧ ¬ junkref(str, st[r -- fs '] .refval, st) ⊦ r = jvmref, st[r -- mkfs(class, ty0, fieldvar) '] .refval = jvmref, st[st[r -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type ≤ ty0 ∧ validref(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval, ty0, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), st[r -- _type] .type ≤ ty, is_obj(str, r, st), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), ∀ fs. ¬ fs ' ∈ instfields(st[r -- _type] .type .class) ∨ ¬ is_referencevalue(st[r -- fs ']) ∨ st[r -- fs '] .refval = jvmref ∨ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∧ ¬ junkref(str, st[r -- fs '] .refval, st) ⊦ r = jvmref, r0 = jvmref, st[r0 -- _type] .type ≤ ty0 ∧ validref(str, r0, ty0, st)

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)]]