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Proof step 22 from proof band-011x-is-unsigned-fix (previous step)

1 + i→n(i) - 2 = i→n(i) - 1, 2 ^ i0 + j = 0, # int2bits(j) < # int2bits(~ j), j < 0, # int2bits(j) < i→n(i), 0 < i, i→n(i) < # int2bits(~ j), # int2bits(j) + 1 < # int2bits(~ j) ⊦ j + 2 ^ n→i(i→n(i) - 1) = 0, j = 0, band(j, 2 ^ i - 1) = bits2uint(fillsgn(i→n(i), int2bits(j))), i = 0

User applied rule cut formula

And closed the goal!

Rule argument

fma: j = ~(2 ^ i0)

Additional information

Used simplifier rules: ⊦ ~ i = j ↔ i + j = 0;% ⊦ ~ i + i = 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i + ~ j = i - j;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + 0 = i;% ⊦ ~ i = 0 ↔ i = 0;% ⊦ ~ ~ i = i;% ⊦ ~ i < 0 ↔ 0 < i;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;%0 ≤ i ⊦ int2bits(~(2 ^ i)) = true ' + mklist(false, i→n(i));% ⊦ 0 ≤ j → 2 ^ j ≠ 0;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ # mklist(boolvar, n) = n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;%0 ≤ i ⊦ int2bits(2 ^ i) = false ' + true ' + mklist(false, i→n(i));% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ 0 ≤ i → abs(i) = i;% ⊦ ¬ i < i;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used formulas: j = ~(2 ^ i0)