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Proof step 50 from proof fits-put-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ 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 49:
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, sks0, st), is_bytevalue(st[r1 -- fs ']), ∀ 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)], junkref(str, r, st)

Rule argument

[crewrite-arg: fits-storekeys-rec , F , [st, sks, sk, r] → [st, sks0, sk, r] ]

Additional information

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