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Proof step 21 from proof putbar-getbar-le (previous step)

∀ j, r, i, st. 0 ≤ j ∧ j ≤ n→i(# bytes0) → getbytearray(r, i, j, putByteArray(bytes0, r, i, st)) = firstn(i→n(j), bytes0), 0 ≤ j, j ≤ n→i(# (by + bytes0)) ⊦ getbytearray(r, i, j, putByteArray(by + bytes0, r, i, st)) = firstn(i→n(j), by + bytes0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
j ≤ 1 + n→i(# bytes0), 0 ≤ j, ∀ j0, r0, i0, st0. ¬ j0 < 0 ∧ ¬ n→i(# bytes0) < j0 → getbytearray(r0, i0, j0, putByteArray(bytes0, r0, i0, st0)) = firstn(i→n(j0), bytes0) ⊦ getbytearray(r, i, j, putByteArray(by ' + bytes0, r, i, st)) = firstn(i→n(j), by ' + bytes0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : i < 0 ⊦ ((* i)) ≤ n→i(n)], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1], [CSIMPSEQ : ⊦ # by ' = 0 +1], [CSIMPSEQ : ⊦ # (bytes + bytes0) = # bytes + # bytes0], [CSIMPSEQ : ⊦ by + bytes = by ' + bytes])]]