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Proof step 13 from proof putByteArray-append (previous step)

0 ≤ j, (~1) ≤ n→i(# bytes1) + j, ∀ j0, bytes0, r0, st0. ¬ j0 + n→i(# bytes1) < 0 ∧ ¬ j0 < 0 → putByteArray(bytes0, r0, j0 + n→i(# bytes1), putByteArray(bytes1, r0, j0, st0)) = putByteArray(bytes1 + bytes0, r0, j0, st0) ⊦ putByteArray(bytes, r, (1 + n→i(# bytes1)) + j, putByteArray(by ' + bytes1, r, j, st)) = putByteArray((by ' + bytes1) + bytes, r, j, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ bytes ≠ [] → putByteArray(bytes, r, i, st) = (putByteArray(bytes .rest, r, i + 1, st)[r -- i ', byteval(bytes .first)])
Proof step 12:
by ' + bytes1 ≠ [], 0 ≤ j, (~1) ≤ n→i(# bytes1) + j, ∀ j0, bytes0, r0, st0. ¬ j0 + n→i(# bytes1) < 0 ∧ ¬ j0 < 0 → putByteArray(bytes0, r0, j0 + n→i(# bytes1), putByteArray(bytes1, r0, j0, st0)) = putByteArray(bytes1 + bytes0, r0, j0, st0) ⊦ putByteArray(bytes, r, (1 + n→i(# bytes1)) + j, putByteArray((by ' + bytes1) .rest, r, j + 1, st)[r -- j ', byteval((by ' + bytes1) .first)]) = putByteArray((by ' + bytes1) + bytes, r, j, st)

Rule argument

[crewrite-arg: putBar-rec , F , [st, i, r, bytes] → [st, j, r, by ' + bytes1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = []], [CSIMPSEQ : ⊦ by ' ≠ []], [CSIMPSEQ : ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1])], [EXTRATERMS : (st, j, r, by ' + bytes1)]]