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Proof step 78 from proof uint2bits-mod2pot (previous step)

¬ i→n(i0) ≤ # uint2bits(j / 2).rest, j % 2 = 0, uint2bits((j / 2) % 2 ^ i0) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest)), mklist(false, # lastn(i→n(i0), uint2bits(j / 2).rest)) = lastn(i→n(i0), uint2bits(j / 2).rest), 0 < (j / 2) % 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 79:
j % 2 = 0, uint2bits((j / 2) % 2 ^ i0) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest)), mklist(false, # lastn(i→n(i0), uint2bits(j / 2).rest)) = lastn(i→n(i0), uint2bits(j / 2).rest), 0 < i0, 0 < j, 2 ^ i0 * 2 < j, # uint2bits(j / 2).rest < i→n(i0), 0 < (j / 2) % 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

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ m < n → n ≠ 0; (forward)% ⊦ ¬ m ≤ n ↔ n < m;