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Proof step 19 from proof putBar-lastrec (previous step)

by0 ' + bytes0 ≠ [], ∀ by, r, i, st. putByteArray(bytes0 + by ', r, i, st) = (putByteArray(bytes0, r, i, st)[r -- (i + n→i(# bytes0)) ', byteval(by)]) ⊦ (putByteArray(bytes0 + by ', r, i + 1, st)[r -- i ', byteval(by0)]) = (putByteArray((by0 ' + bytes0) .rest, r, i + 1, st)[r -- i ', byteval((by0 ' + bytes0) .first)][r -- ((1 + n→i(# bytes0)) + i) ', byteval(by)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
∀ by, r, i, st. putByteArray(bytes0 + by ', r, i, st) = (putByteArray(bytes0, r, i, st)[r -- (i + n→i(# bytes0)) ', byteval(by)]) ⊦ (putByteArray(bytes0 + by ', r, i + 1, st)[r -- i ', byteval(by0)]) = (putByteArray(bytes0, r, i + 1, st)[r -- i ', byteval(by0)][r -- ((1 + n→i(# bytes0)) + i) ', byteval(by)])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ by ' + bytes ≠ []], [CSIMPSEQ : ⊦ (by ' + bytes) .first = by], [CSIMPSEQ : ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1], [CSIMPSEQ : ⊦ (by ' + bytes) .rest = bytes])]]