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Proof step 36 from proof bor-2pot-plus (previous step)

# bits ≠ 0 ∧ # uint2bits(j) ≠ 0 ∧ ¬ uint2bits(j).first, # int2bits(j0) = i→n(i) + 1, int2bits(j0) = boolvar ' + bits, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ j0, boolvar ∈ int2bits(j0), i→n(i) ≤ # bits ⊦ i = 0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2uint(uint2bits(j)) * 2 ^ n→i(# bits) + bits2uint(bits) = j * 2 ^ i + j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
# int2bits(j0) = i→n(i) + 1, int2bits(j0) = boolvar ' + bits, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ j0, boolvar ∈ int2bits(j0), i→n(i) ≤ # bits ⊦ i = 0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2uint(bits) + 2 ^ n→i(# bits) * j = j * 2 ^ i + j0, bits = []

Rule argument

Additional information

Used simplifier rules: ⊦ 0 ≤ j → ¬ uint2bits(j).first;%0 ≤ i ⊦ uint2bits(i) ≠ [];% ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ # bits = 0 ↔ bits = [];% ⊦ 0 ≤ i → bits2uint(uint2bits(i)) = i;