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Proof step 7 from proof putByteArray-put-switch (previous step)

j < i, 0 ≤ j, 0 ≤ i, 0 < i, ¬ i + 1 ≤ j ∧ ¬ j < 0 ∧ ¬ i + 1 ≤ 0 → putByteArray(bytes0, r, i + 1, st[r -- j ', byteval(by)]) = (putByteArray(bytes0, r, i + 1, st)[r -- j ', byteval(by)]), ∀ j0, i0, r0, st0, by1. ¬ i0 ≤ j0 ∧ ¬ j0 < 0 ∧ ¬ i0 ≤ 0 → putByteArray(bytes0, r0, i0, st0[r0 -- j0 ', byteval(by1)]) = (putByteArray(bytes0, r0, i0, st0)[r0 -- j0 ', byteval(by1)]) ⊦ (putByteArray(bytes0, r, i + 1, st[r -- j ', byteval(by)])[r -- i ', byteval(by0)]) = (putByteArray(bytes0, r, i + 1, st)[r -- i ', byteval(by0)][r -- j ', byteval(by)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
putByteArray(bytes0, r, i + 1, st[r -- j ', byteval(by)]) = (putByteArray(bytes0, r, i + 1, st)[r -- j ', byteval(by)]), j < i, 0 ≤ j, 0 ≤ i, 0 < i, ∀ j0, i0, r0, st0, by1. ¬ i0 ≤ j0 ∧ ¬ j0 < 0 ∧ ¬ i0 ≤ 0 → putByteArray(bytes0, r0, i0, st0[r0 -- j0 ', byteval(by1)]) = (putByteArray(bytes0, r0, i0, st0)[r0 -- j0 ', byteval(by1)]) ⊦ (putByteArray(bytes0, r, i + 1, st)[r -- j ', byteval(by)][r -- i ', byteval(by0)]) = (putByteArray(bytes0, r, i + 1, st)[r -- i ', byteval(by0)][r -- j ', byteval(by)])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ (~1) ↔ i < 0], [CSIMPSEQ : ⊦ i + ((* j)) ≤ ((* j0)) ↔ i ≤ j0 - j], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j])]]