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Proof step 54 from proof fits-put-03 (previous step)

is_bytevalue(st[r1 -- fs ']), fits(r, sk ' + sks0, st), ∀ 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) ⊦ (st[r1 -- fs ', byteval(by)][r -- (sk ' + sks0)]) = st[r -- (sk ' + sks0)], junkref(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks]
Proof step 7:
¬ sks0 ≠ [], is_bytevalue(st[r1 -- fs ']), fits(r, sk ' + sks0, st), ∀ 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) ⊦ (st[r1 -- fs ', byteval(by)][r -- (sk ' + sks0)]) = st[r -- (sk ' + sks0)], junkref(str, r, st)
Proof step 53:
sks0 ≠ [], is_bytevalue(st[r1 -- fs ']), fits(r, sk ' + sks0, st), ∀ 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) ⊦ (st[r1 -- fs ', byteval(by)][(st[r1 -- fs ', byteval(by)][r -- sk]) .refval -- sks0]) = st[r -- (sk ' + sks0)], 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[r1 -- fs ', byteval(by)]] ,F ,storefuns , ,lookup-rec-01 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sks0, sk, r, st[r1 -- fs ', byteval(by)])]]