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Proof step 46 from proof fits-put-03 (previous step)

st[r -- sk] = refval(r0), fits(r0, sks0, st), is_bytevalue(st[r1 -- fs ']), 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, ∀ st, r1, fs, r, by, str. is_bytevalue(st[r1 -- fs ']) ∧ fits(r, sks0, st) → (st[r1 -- fs ', byteval(by)][r -- sks0]) = st[r -- sks0] ∨ junkref(str, r, st), r ≠ r1 ∨ sk ≠ fs ' ⊦ sks0 = [], (st[r1 -- fs ', byteval(by)][(st[r1 -- fs ', byteval(by)][r -- sk]) .refval -- sks0]) = st[r -- (sk ' + sks0)], r = jvmref, junkref(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks]
Proof step 45:
sks0 ≠ [], st[r -- sk] = refval(r0), fits(r0, sks0, st), is_bytevalue(st[r1 -- fs ']), 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, ∀ st, r1, fs, r, by, str. is_bytevalue(st[r1 -- fs ']) ∧ fits(r, sks0, st) → (st[r1 -- fs ', byteval(by)][r -- sks0]) = st[r -- sks0] ∨ junkref(str, r, st), r ≠ r1 ∨ sk ≠ fs ' ⊦ sks0 = [], (st[r1 -- fs ', byteval(by)][(st[r1 -- fs ', byteval(by)][r -- sk]) .refval -- sks0]) = st[st[r -- sk] .refval -- sks0], r = jvmref, junkref(str, r, st)

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 : ()], [EXTRATERMS : (sks0, sk, r, st)]]