[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 113 from proof uint2bits-add-high (previous step)

2 ^ (i - 1) = 2 ^ i0, j % 2 = 0, 2 ^ i0 = ~((j - 1) / 2), (1 - j) / 2 < 2 ^ i0, 2 ^ (i - 2) < (1 - j) / 2, (1 - j) / 2 < 2 ^ i, 2 ^ i0 + j < 2 ^ i, 2 ^ i0 + j < 0, j < (j - 1) / 2, (2 ^ i0 + j) + 1 < i0, (2 ^ i0 + j) + 1 < 2 ^ i, (2 ^ i0 + j) + 1 < i, 2 ^ i0 + j < i0, 2 ^ i0 + j < i, j + 1 < i0, 0 < i0, j < i0, 0 < 2 ^ i, 1 < 2 ^ i, 2 ^ i0 + 1 < 2 ^ i, 0 < j + 2 ^ i, j + 1 < i, 0 < i, j < i, j + 1 < 2 ^ i, j < 2 ^ i, 0 ≤ 2 ^ i, 0 ≤ j + 2 ^ i, j ≤ 2 ^ i, j < 0, 2 ^ (i - 2) + 1 < 2 ^ i0, ∀ i0, j. i→n(i0) < i→n(i) → true → j < 0 ∧ 0 < i0 ∧ 2 ^ (i0 - 1) < abs(j) ∧ abs(j) ≤ 2 ^ i0 → uint2bits(j + 2 ^ i0) = sgn(int2bits(j).rest) ⊦ (1 - j) / 2 = 2 ^ i0, i = 1, j = 0, j = ~1, j + 2 ^ i = 1, i0 = 0

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 3 flags: discard

Additional information

Used simplifier rules: ⊦ ~ i = j ↔ i + j = 0;%j0 ≠ 0 ⊦ (i - j) / j0 + (j - i) / j0 = 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;