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Proof step 61 from proof uint2bits-mod2pot (previous step)

uint2bits(i1 % 2 ^ i0) = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest)), 0 ≤ i0, 0 ≤ i1, 2 ^ i0 < i1, 0 < i1, ∀ j0, i. i→n(j0) < i→n(i1 * 2 + 0) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ i1 % 2 ^ i0 ≠ 0, ~1 = i0, uint2bits(i1 % 2 ^ i0 * 2) = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest) + false ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 62:
i1 % 2 ^ i0 = 0, false ' = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest)), 0 < i1, 2 ^ i0 < i1, 0 ≤ i1, 0 ≤ i0, ∀ j0, i. i→n(j0) < i→n(i1 * 2 + 0) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ ~1 = i0, false ' = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest) + false ')

Rule argument

Additional information

Used simplifier rules: uint2bits-zero: ⊦ uint2bits(0) = false ';% ⊦ i < j ∧ i = i0 → i0 < j; (forward)