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Proof step 80 from proof uint2bits-mod2pot (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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