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Proof step 72 from proof uint2bits-mod2pot (previous step)

¬ (¬ false) ∈ lastn(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)), 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)) ⊦ uint2bits((j / 2) % 2 ^ i0) + false ' = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest) + false '), ~1 = i0, j = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 73:
j % 2 = 0, uint2bits((j / 2) % 2 ^ i0) = sgn(false ' + 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, true ∈ lastn(i→n(i0), uint2bits(j / 2).rest)

Rule argument

Additional information

Used simplifier rules: uint2bits-empty: 0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ bits = bits0 + bits ↔ bits0 = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ sgn(false ' + false ') = false ';%⊦ ¬ (¬ boolvar) ∈ bits → sgn(boolvar ' + bits + bits0) = sgn(boolvar ' + bits0);