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Proof step 25 from proof putBar-rew (previous step)

j < i ∨ i + n→i(# bytes) ≤ j ⊦ sk = j ', (putByteArray(bytes, r, i, st)[r -- sk]) = (putByteArray(bytes, r, i, st[r -- j ', val])[r -- sk])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ is_fskey(sk) → (putByteArray(bytes, r, i, st)[r -- sk]) = st[r -- sk]
Proof step 23:
¬ is_fskey(sk), j < i ∨ i + n→i(# bytes) ≤ j ⊦ sk = j ', (putByteArray(bytes, r, i, st)[r -- sk]) = (putByteArray(bytes, r, i, st[r -- j ', val])[r -- sk])
Proof step 24:
⊦ is_fskey(sk) → (putByteArray(bytes, r, i, st)[r0 -- sk]) = st[r0 -- sk]

Rule argument

[crewrite-arg: putBar-at , F , [sk, st, i, r, bytes] → [sk, st, i, r, bytes] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])], [EXTRATERMS : (sk, st, i, r, bytes)]]