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Proof step 60 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)) ⊦ ~1 = i0, uint2bits(i1 % 2 ^ i0 * 2) = sgn(false ' + lastn(i→n(i0), uint2bits(i1).rest) + false '), i1 % 2 ^ i0 ≠ 0 ∧ (abs(i1 % 2 ^ i0) ≠ 1 ∨ i1 % 2 ^ i0 ≠ 2)

User applied rule case distinction

And obtained the following new goals

Proof step 61:
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 ')

Rule argument

pos: right 3

Additional information

Used simplifier rules: uint2bits-pos-num: 1 < i ⊦ uint2bits((* i)) = uint2bits(i / 2) + (i % 2 = 1);%uint2bits-one: ⊦ uint2bits(1) = false + true;% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ bits + boolvar = bits + boolvar ';