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Proof step 47 from proof fits-put-01 (previous step)

st[r -- sk] = refval(r0), fits(r0, sks0, st), okarray(r1, byte_type, st), is_referencevalue(st[r -- (sk ' + sks0)]), is_valid_ref(str, r, st), r1 ∈ st, r ≠ r1 ∨ sk ≠ i ', ∀ st, r, r1, str, i, by. is_referencevalue(st[r -- sks0]) ∧ okarray(r1, byte_type, st) ∧ fits(r, sks0, st) ∧ r1 ∈ st ∧ is_valid_ref(str, r, st) → r1 = jvmref ∨ r = jvmref ∨ fits(r, sks0, st[r1 -- i ', byteval(by)]) ∨ junkref(str, r, st), is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval, is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class) ⊦ r = jvmref, r1 = jvmref, junkref(str, r, st), (is_arraytype(st[r -- _type] .type) → ¬ is_fskey(sk) ∧ ¬ sk .index < 0 ∧ ¬ st[r -- _length] .intval ≤ sk .index) ∧ fits(r0, sks0, st[r1 -- i ', byteval(by)])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks] ,[sks, sk, r, st] → [sks0, sk, r, st] ,F ,storefuns , ,lookup-rec-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sks + [] = sks], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ st[r -- sk '] = st[r -- sk]], [CSIMPSEQ : ⊦ st[r -- []] = refval(r)], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ is_arraytype (st[r -- _type] .type) ∧ r ≠ jvmref → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))], [CSIMPSEQ : ⊦ is_arraytype(ty) → ¬ is_classtype(ty)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (sks0, sk, r, st)]]