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Proof step 8 from proof putByteArray-append (previous step)

0 ≤ j, (~1) ≤ n→i(# bytes1) + j, ∀ j0, bytes0, r0, st0. ¬ j0 + n→i(# bytes1) < 0 ∧ ¬ j0 < 0 → putByteArray(bytes0, r0, j0 + n→i(# bytes1), putByteArray(bytes1, r0, j0, st0)) = putByteArray(bytes1 + bytes0, r0, j0, st0) ⊦ putByteArray(bytes, r, (1 + n→i(# bytes1)) + j, putByteArray(bytes1, r, j + 1, st)[r -- j ', byteval(by)]) = (putByteArray(bytes1 + bytes, r, j + 1, st)[r -- j ', byteval(by)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 ≤ j ∧ 0 ≤ i ∧ j < i → putByteArray(bytes, r, i, st[r -- j ', byteval(by)]) = (putByteArray(bytes, r, i, st)[r -- j ', byteval(by)])
Proof step 7:
0 ≤ j ∧ 0 ≤ (1 + n→i(# bytes1)) + j ∧ j < (1 + n→i(# bytes1)) + j, 0 ≤ j, (~1) ≤ n→i(# bytes1) + j, ∀ j0, bytes0, r0, st0. ¬ j0 + n→i(# bytes1) < 0 ∧ ¬ j0 < 0 → putByteArray(bytes0, r0, j0 + n→i(# bytes1), putByteArray(bytes1, r0, j0, st0)) = putByteArray(bytes1 + bytes0, r0, j0, st0) ⊦ (putByteArray(bytes, r, (1 + n→i(# bytes1)) + j, putByteArray(bytes1, r, j + 1, st))[r -- j ', byteval(by)]) = (putByteArray(bytes1 + bytes, r, j + 1, st)[r -- j ', byteval(by)])

Rule argument

[crewrite-arg: putByteArray-put-switch , F , [by, j, st, i, r, bytes] → [by, j, putByteArray(bytes1, r, j + 1, st), (1 + n→i(# bytes1)) + j, r, bytes] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0])], [EXTRATERMS : (by, j, putByteArray(bytes1, r, j + 1, st), (1 + n→i(# bytes1)) + j, r, bytes)]]