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Proof step 20 from proof intshiftleft-is-mult-01 (previous step)

0 ≤ j, i < 0 ⊦ (i + 1) * 2 ^ abs(band(j, 31)) = 2 ^ abs(band(j, 31)) + i * 2 ^ band(j, 31), band(j, 31) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ 0 ≤ j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = j % (i + 1)
Proof step 22:
¬(0 ≤ j ∧ ¬ false ∈ int2bits(31).rest ∧ 0 ≤ 31), 0 ≤ j, i < 0 ⊦ (i + 1) * 2 ^ abs(band(j, 31)) = 2 ^ abs(band(j, 31)) + i * 2 ^ band(j, 31), band(j, 31) = 0
Proof step 25:
0 ≤ j ∧ ¬ false ∈ int2bits(31).rest ∧ 0 ≤ 31, 0 ≤ j, i < 0 ⊦ (i + 1) * 2 ^ abs(j % (31 + 1)) = 2 ^ abs(j % (31 + 1)) + i * 2 ^ (j % (31 + 1)), j % (31 + 1) = 0

Rule argument

name: band-011x-pos-02 rotate: F subst: [i, j] → [31, j]

Additional information

Used terms: 31, j