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Proof step 16 from proof putbar-put-override (previous step)

∀ i, j, r, st, by. 0 ≤ i ∧ 0 ≤ j ∧ i < j + n→i(# bytes0) ∧ j ≤ i ∧ 0 < j + n→i(# bytes0) → bytes0 = [] ∨ putByteArray(bytes0, r, j, st[r -- i ', byteval(by)]) = putByteArray(bytes0, r, j, st), 0 ≤ i, 0 ≤ j, i < j + n→i(# (by0 + bytes0)), j ≤ i, 0 < j + n→i(# (by0 + bytes0)) ⊦ by0 + bytes0 = [], putByteArray(by0 + bytes0, r, j, st[r -- i ', byteval(by)]) = putByteArray(by0 + bytes0, r, j, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
0 ≤ n→i(# bytes0) + j, j ≤ i, i ≤ n→i(# bytes0) + j, 0 ≤ j, 0 ≤ i, ∀ i0, j0, r0, st0, by1. ¬ i0 < 0 ∧ ¬ j0 < 0 ∧ ¬ j0 + n→i(# bytes0) ≤ i0 ∧ ¬ i0 < j0 ∧ ¬ j0 + n→i(# bytes0) ≤ 0 → bytes0 = [] ∨ putByteArray(bytes0, r0, j0, st0[r0 -- i0 ', byteval(by1)]) = putByteArray(bytes0, r0, j0, st0) ⊦ putByteArray(by0 ' + bytes0, r, j, st[r -- i ', byteval(by)]) = putByteArray(by0 ' + bytes0, r, j, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ 0 ≤ n→i(n)], [CSIMPSEQ : ⊦ i ≤ i + j ↔ 0 ≤ j], [CSIMPFORWARD : ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i < j + 1 ↔ 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 : ⊦ # by ' = 0 +1], [CSIMPSEQ : ⊦ # (bytes + bytes0) = # bytes + # bytes0], [CSIMPSEQ : ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1], [CSIMPSEQ : ⊦ by ' + bytes ≠ []], [CSIMPSEQ : ⊦ by + bytes = by ' + bytes])]]