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Proof step 37 from proof uint2bits-mod2pot (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
(j / 2) % 2 ^ i0 = 0, j % 2 = 1, false ' = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).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(j / 2).rest) + true ')

Rule argument

Additional information

Used simplifier rules: uint2bits-zero: ⊦ uint2bits(0) = false ';%uint2bits-one: ⊦ uint2bits(1) = false + true;% ⊦ 0 < j → i % j < j;% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ i < j ∧ i = i0 → i0 < j; (forward)