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Proof step 10 from proof putbar-override (previous step)

∀ j, j0, bytes, r1, st. j ≤ j0 ∧ j0 + n→i(# bytes1) ≤ j + n→i(# bytes) ∧ 0 ≤ j ∧ 0 ≤ j0 → putByteArray(bytes, r1, j, putByteArray(bytes1, r1, j0, st)) = putByteArray(bytes, r1, j, st), j ≤ j0, j0 + n→i(# (by + bytes1)) ≤ j + n→i(# bytes), 0 ≤ j, 0 ≤ j0 ⊦ putByteArray(bytes, r1, j, putByteArray(by + bytes1, r1, j0, st)) = putByteArray(bytes, r1, j, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
0 ≤ j, 0 ≤ j0, j ≤ j0, n→i(# bytes1) + j0 < j + n→i(# bytes), ∀ j1, j2, bytes0, r, st0. ¬ j2 < j1 ∧ ¬ j1 + n→i(# bytes0) < j2 + n→i(# bytes1) ∧ ¬ j1 < 0 ∧ ¬ j2 < 0 → putByteArray(bytes0, r, j1, putByteArray(bytes1, r, j2, st0)) = putByteArray(bytes0, r, j1, st0) ⊦ putByteArray(bytes, r1, j, putByteArray(by ' + bytes1, r1, j0, st)) = putByteArray(bytes, r1, j, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [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])]]