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Proof step 11 from proof putBar-rew-01 (previous step)

∀ r, i, st, r0, fs, val. putByteArray(bytes0, r, i, st[r0 -- fs ', val]) = (putByteArray(bytes0, r, i, st)[r0 -- fs ', val]) ⊦ putByteArray(by ' + bytes0, r, i, st[r0 -- fs ', val]) = (putByteArray(by ' + bytes0, r, i, st)[r0 -- fs ', val])

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 10:
by ' + bytes0 ≠ [], ∀ r, i, st, r0, fs, val. putByteArray(bytes0, r, i, st[r0 -- fs ', val]) = (putByteArray(bytes0, r, i, st)[r0 -- fs ', val]) ⊦ (putByteArray((by ' + bytes0) .rest, r, i + 1, st[r0 -- fs ', val])[r -- i ', byteval((by ' + bytes0) .first)]) = (putByteArray(by ' + bytes0, r, i, st)[r0 -- fs ', val])

Rule argument

[crewrite-arg: putBar-rec , F , [st, i, r, bytes] → [st[r0 -- fs ', val], i, r, by ' + bytes0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = []], [CSIMPSEQ : ⊦ by ' ≠ []], [CSIMPSEQ : ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1])], [EXTRATERMS : (st[r0 -- fs ', val], i, r, by ' + bytes0)]]