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Proof step 7 from proof putbar-refval (previous step)

(putByteArray(by ' + bytes0, r1, i, st)[r1 -- i0 ']) = refval(r0), ∀ r1, i, st, i0, r0. (putByteArray(bytes0, r1, i, st)[r1 -- i0 ']) = refval(r0) → st[r1 -- i0 '] = refval(r0) ⊦ st[r1 -- i0 '] = refval(r0)

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 6:
by ' + bytes0 ≠ [], (putByteArray((by ' + bytes0) .rest, r1, i + 1, st)[r1 -- i ', byteval((by ' + bytes0) .first)][r1 -- i0 ']) = refval(r0), ∀ r1, i, st, i0, r0. (putByteArray(bytes0, r1, i, st)[r1 -- i0 ']) = refval(r0) → st[r1 -- i0 '] = refval(r0) ⊦ st[r1 -- i0 '] = refval(r0)

Rule argument

[crewrite-arg: putBar-rec , F , [st, i, r, bytes] → [st, i, r1, by ' + bytes0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = []], [CSIMPSEQ : ⊦ by ' ≠ []], [CSIMPSEQ : ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1])], [EXTRATERMS : (st, i, r1, by ' + bytes0)]]