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Proof step 20 from proof putbar-getbar-le (previous step)

j ≤ 1 + n→i(# bytes0), 0 ≤ j, ∀ j0, r0, i0, st0. ¬ j0 < 0 ∧ ¬ n→i(# bytes0) < j0 → getbytearray(r0, i0, j0, putByteArray(bytes0, r0, i0, st0)) = firstn(i→n(j0), bytes0) ⊦ getbytearray(r, i, j, putByteArray(by ' + bytes0, r, i, st)) = firstn(i→n(j), by ' + bytes0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ bytes ≠ [] → putByteArray(bytes, r, i, st) = (putByteArray(bytes .rest, r, i + 1, st)[r -- i ', byteval(bytes .first)])
Proof step 19:
by ' + bytes0 ≠ [], j ≤ 1 + n→i(# bytes0), 0 ≤ j, ∀ j0, r0, i0, st0. ¬ j0 < 0 ∧ ¬ n→i(# bytes0) < j0 → getbytearray(r0, i0, j0, putByteArray(bytes0, r0, i0, st0)) = firstn(i→n(j0), bytes0) ⊦ getbytearray(r, i, j, putByteArray((by ' + bytes0) .rest, r, i + 1, st)[r -- i ', byteval((by ' + bytes0) .first)]) = firstn(i→n(j), by ' + bytes0)

Rule argument

[crewrite-arg: putBar-rec , F , [st, i, r, bytes] → [st, i, r, by ' + bytes0] ]

Additional information

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