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Proof step 41 from proof intshiftleft-is-mult-01 (previous step)

0 < i, j < 0 ⊦ band(j, 31) = 0, i = 0, 2 ^ abs(band(j, 31)) = 2 ^ band(j, 31)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ j < 0 ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = (j + 1) % (i + 1) + i
Proof step 43:
¬(j < 0 ∧ ¬ false ∈ int2bits(31).rest ∧ 0 ≤ 31), 0 < i, j < 0 ⊦ band(j, 31) = 0, i = 0, 2 ^ abs(band(j, 31)) = 2 ^ band(j, 31)
Proof step 46:
j < 0 ∧ ¬ false ∈ int2bits(31).rest ∧ 0 ≤ 31, 0 < i, j < 0 ⊦ (j + 1) % (31 + 1) + 31 = 0, i = 0, 2 ^ abs((j + 1) % (31 + 1) + 31) = 2 ^ ((j + 1) % (31 + 1) + 31)

Rule argument

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

Additional information

Used terms: 31, j