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Proof step 39 from proof uint2bits-mod2pot (previous step)

j = i1 * 2 + j1 ∧ 0 ≤ j1 ∧ j1 < 2 ∧ 0 < 2, i1 % 2 ^ i0 = 0, j1 = 1, false ' = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest)), 0 ≤ j, 0 < 2 ^ i0, 0 ≤ i0, 0 < j, 2 ^ i0 * 2 < j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ ~1 = i0, j = 1, false ' + true ' = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest) + true ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
false ' = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest)), i1 % 2 ^ i0 = 0, 0 < i1, 2 ^ i0 ≤ i1, 0 ≤ i0, 0 < 2 ^ i0, ∀ j0, i. i→n(j0) < i→n(i1 * 2 + 1) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ i1 = 0, ~1 = i0, false ' + true ' = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest) + true ')

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < j → i % j < j;% ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0);% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 2 * i = 0 ↔ i = 0;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;