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Proof step 10 from proof putbar-getbar-le (previous step)

0 ≤ i1, i1 ≤ n→i(# bytes0), ∀ j0, r0, i0, st0. ¬ j0 < 0 ∧ ¬ n→i(# bytes0) < j0 → getbytearray(r0, i0, j0, putByteArray(bytes0, r0, i0, st0)) = firstn(i→n(j0), bytes0) ⊦ (~1) = i1, getbytearray(r, i + 1, i1, putByteArray(bytes0, r, i + 1, st)[r -- i ', byteval(by)]) = firstn(i→n(i1), bytes0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ i0 < i → getbytearray(r, i, j, st[r0 -- i0 ', val]) = getbytearray(r, i, j, st)
Proof step 9:
i < i + 1, 0 ≤ i1, i1 ≤ n→i(# bytes0), ∀ j0, r0, i0, st0. ¬ j0 < 0 ∧ ¬ n→i(# bytes0) < j0 → getbytearray(r0, i0, j0, putByteArray(bytes0, r0, i0, st0)) = firstn(i→n(j0), bytes0) ⊦ (~1) = i1, getbytearray(r, i + 1, i1, putByteArray(bytes0, r, i + 1, st)) = firstn(i→n(i1), bytes0)

Rule argument

[crewrite-arg: getbar-put-lower , F , [val, i0, r0, st, j, i, r] → [byteval(by), i, r, putByteArray(bytes0, r, i + 1, st), i1, i + 1, r] ]

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(by), i, r, putByteArray(bytes0, r, i + 1, st), i1, i + 1, r)]]