[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 90 from proof uint2bits-add-high (previous step)

uint2bits(2 ^ (i - 1) - 2 ^ i0) = false ', 2 ^ (i - 1) + ~(2 ^ i0) * 2 < 0, 0 ≤ i, (2 ^ (i - 1) + ~(2 ^ i0) * 2) + 1 < i, 2 ^ (i - 1) + ~(2 ^ i0) * 2 < i, ~(2 ^ i0) * 2 + 1 < i, 2 ^ (i - 1) + ~(2 ^ i0) * 2 < 2 ^ i, 0 < ~(2 ^ i0) * 2 + 2 ^ i, i ≤ i0, 1 < 2 ^ i, 0 < 2 ^ i, 1 < i, 0 < i, 0 < i0, ~(2 ^ i0) * 2 < i0, 2 ^ (i - 1) + ~(2 ^ i0) * 2 < i0, ~(2 ^ i0) * 2 + 1 < i0, (2 ^ (i - 1) + ~(2 ^ i0) * 2) + 1 < i0, abs(~(2 ^ i0) * 2 - 1) / 2 < 2 ^ i, 2 ^ (i - 2) < abs(~(2 ^ i0) * 2 - 1) / 2, abs(~(2 ^ i0) * 2 - 1) / 2 ≤ 2 ^ (i - 1), ~(2 ^ i0) < 0, 0 ≤ 2 ^ i0 * 2 + 2 ^ i, 2 ^ i0 * 2 ≤ 2 ^ i, 0 ≤ 2 ^ i, 2 ^ (i - 1) + 1 < 2 ^ i0 * 2 + 2 ^ i, 0 < 2 ^ i + 2 ^ i0 * 2, 1 < 2 ^ i0 * 2 + 2 ^ i, 0 < i + 2 ^ i0 * 2, ∀ 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) ⊦ i = 1, i0 = 0, 2 ^ i = 1 + 2 ^ i0 * 2, ~(2 ^ i0) * 2 - 1 < 0, ~(2 ^ i0) * 2 ≤ 0 ∧ ~(2 ^ i0) * 2 ≠ 0

User applied rule weakening

And obtained the following new goals

Rule argument

poslist: left 1, left 2, left 3, left 4, left 5, left 6, left 7, left 8, left 9, left 10, left 11, left 12, left 13, left 14, left 15, left 16, left 17, left 18, left 19, left 20, left 21

Additional information