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Proof step 41 from proof uint2bits-mod2pot (previous step)

i1 = i2 * 2 ^ i0 + j ∧ 0 ≤ j ∧ j < 2 ^ i0, false ' = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest)), j = 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 ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
false ' = sgn(false ' + lastn(i→n(i0), uint2bits(i2 * 2 ^ i0).rest)), 0 ≤ i0, 0 < 2 ^ i0, 0 < i2, ∀ j0, i. i→n(j0) < i→n((i2 * 2 ^ i0 + 0) * 2 + 1) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ i2 = 0, ~1 = i0, false ' + true ' = sgn(false ' + lastn(i→n(i0), uint2bits(i2 * 2 ^ i0).rest) + true ')

Rule argument

Additional information

Used simplifier rules: ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 0 < i → (i ≤ i * j ↔ 1 ≤ j);% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 ≤ j → 2 ^ j ≠ 0;% ⊦ i * j = 0 ↔ i = 0 ∨ j = 0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 0 = i;