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Proof step 34 from proof int2int-neg (previous step)

j ≤ 4 * 2 ^ i, j < 4 * 2 ^ i, j < 3 * 2 ^ i, j ≤ 3 * 2 ^ i, 2 ^ i + j ≤ 0, 0 < 2 ^ i * 2 + j, 2 ^ i + j ≤ i + 2, 2 ^ i + j < i + 2, j < i + 2, j < 0, j < 2 ^ i, j + 1 < 2 ^ i, j ≤ i, 0 ≤ i, j + 1 < 4 * 2 ^ i, 0 ≤ 4 * 2 ^ i + j, 0 < 4 * 2 ^ i + j, 2 ^ i + j ≤ i, j < i, j ≤ i + 2, j ≤ 0, j ≤ 2 ^ i, 0 ≤ 2 ^ i, 0 < 2 ^ i ⊦ 4 * 2 ^ i = 2 ^ (n→i(# uint2bits(4 * 2 ^ i + j)) - 1)

User applied rule cut formula

And obtained the following new goals

Proof step 35:
j ≤ 4 * 2 ^ i, j < 4 * 2 ^ i, j < 3 * 2 ^ i, j ≤ 3 * 2 ^ i, 2 ^ i + j ≤ 0, 0 < 2 ^ i * 2 + j, 2 ^ i + j ≤ i + 2, 2 ^ i + j < i + 2, j < i + 2, j < 0, j < 2 ^ i, j + 1 < 2 ^ i, j ≤ i, 0 ≤ i, j + 1 < 4 * 2 ^ i, 0 ≤ 4 * 2 ^ i + j, 0 < 4 * 2 ^ i + j, 2 ^ i + j ≤ i, j < i, j ≤ i + 2, j ≤ 0, j ≤ 2 ^ i, 0 ≤ 2 ^ i, 0 < 2 ^ i ⊦ j = ~(3 * 2 ^ i), 4 * 2 ^ i = 2 ^ (n→i(# uint2bits(4 * 2 ^ i + j)) - 1)

Rule argument

fma: j = ~(3 * 2 ^ i)

Additional information

Used simplifier rules: uint2bits-2pot: 0 ≤ i ⊦ uint2bits(2 ^ i) = false ' + true ' + mklist(false, i→n(i));% ⊦ i + ~ j = i - j;% ⊦ i * j - i * j0 = i * (j - j0);% ⊦ 1 * i = i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ # mklist(boolvar, n) = n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ 0 ≤ i → n→i(i→n(i)) = i;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0);% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ i * j + i * j0 = i * (j + j0);% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ 0 < i ∧ 0 < j → 0 < i + j;% ⊦ i - j ≤ i0 ↔ i ≤ j + i0;% ⊦ i + 0 = i;% ⊦ 0 < i → (i ≤ i * j ↔ 1 ≤ j);% ⊦ i * ~1 = ~ i;% ⊦ 0 < ~ i ↔ i < 0;% ⊦ ¬ 2 ^ i < 0; Used formulas: j = ~(3 * 2 ^ i)