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Proof step 9 from proof hasSharing-object-rec (previous step)

st[r0 -- sks] = refval(r1), st[r -- sk] = refval(r0), st[r -- _type] .type = mkclasstype(class), st[r0 -- sks0] = refval(r1), fits(r0, sks0, st), fits(r0, sks, st), sk ∈ instfields(class) ⊦ sks = [], r = jvmref, r1 = jvmref, sks0 = sks, sks0 = [], fits(r, sk ' + sks0, st) ∧ fits(r, sk ' + sks, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ fits(r, sk ' + sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ (is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval) ∧ fits(st[r -- sk] .refval, sks, st)
Proof step 8:
st[r0 -- sks] = refval(r1), st[r -- sk] = refval(r0), st[r -- _type] .type = mkclasstype(class), st[r0 -- sks0] = refval(r1), fits(r0, sks0, st), fits(r0, sks, st), sk ∈ instfields(class) ⊦ sks = [], r = jvmref, r1 = jvmref, sks0 = sks, sks0 = [], fits(r, sk ' + sks0, st) ∧ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ (is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval) ∧ fits(st[r -- sk] .refval, sks, st)

Rule argument

[crewrite-arg: fits-storekeys-rec , F , [st, sks, sk, r] → [st, sks, sk, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, sks, sk, r)]]