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Proof step 26 from proof putBar-lastrec (conclusion)

⊦ putByteArray(bytes + by ', r, i, st) = putByteArray(bytes, r, i, st[r -- (i + n→i(# bytes)) ', byteval(by)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ j < i ∨ i + n→i(# bytes) ≤ j → (putByteArray(bytes, r, i, st)[r -- j ', val]) = putByteArray(bytes, r, i, st[r -- j ', val])
Proof step 25:
i + n→i(# bytes) < i ∨ i + n→i(# bytes) ≤ i + n→i(# bytes) ⊦ putByteArray(bytes + by ', r, i, st) = (putByteArray(bytes, r, i, st)[r -- (i + n→i(# bytes)) ', byteval(by)])

Rule argument

[crewrite-arg: putBar-rew , T , [val, j, st, i, r, bytes] → [byteval(by), i + n→i(# bytes), st, i, r, bytes] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j ≤ i0 + j ↔ i ≤ i0], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < i])], [EXTRATERMS : (byteval(by), i + n→i(# bytes), st, i, r, bytes)]]