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Proof step 15 from proof putBar-lastrec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ j < i ∨ i + n→i(# bytes) ≤ j → (putByteArray(bytes, r, i, st)[r -- j ', val]) = putByteArray(bytes, r, i, st[r -- j ', val])
Proof step 14:
i < i + 1 ∨ (i + 1) + n→i(# (bytes0 + by ')) ≤ i, (putByteArray(bytes0 + by ', r, i + 1, st)[r -- i ', byteval(by0)]) = (putByteArray(bytes0, r, i + 1, st[r -- i ', byteval(by0)])[r -- ((i + 1) + n→i(# bytes0)) ', byteval(by)]) ⊦ (putByteArray(bytes0 + by ', r, i + 1, st)[r -- i ', byteval(by0)]) = (putByteArray(bytes0, r, i + 1, st)[r -- ((1 + n→i(# bytes0)) + i) ', byteval(by)][r -- i ', byteval(by0)])

Rule argument

[crewrite-arg: putBar-rew , T , [val, j, st, i, r, bytes] → [byteval(by0), i, st, i + 1, r, bytes0 + by '] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (byteval(by0), i, st, i + 1, r, bytes0 + by ')]]