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Proof step 42 from proof bor-2pot-plus (previous step)

# int2bits(j0) = i→n(i) + 1, int2bits(j0) = false ' + bits, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ j0, i→n(i) ≤ # bits, false ∈ int2bits(j0) ⊦ i = 0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2int(int2bits(j0)) + 2 ^ n→i(# bits) * j = j * 2 ^ i + j0, bits = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# int2bits(j0) = i→n(i) + 1, int2bits(j0) = false ' + bits, 0 < i, j0 < 2 ^ i, 0 < j, 0 ≤ j, 0 < 2 ^ i, 0 ≤ j0, i→n(i) ≤ # bits, false ∈ int2bits(j0) ⊦ bits = [], i = 0, bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], 2 ^ n→i(# bits) = 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0);% ⊦ i + j = i + i0 ↔ j = i0;% ⊦ bits2int(int2bits(i)) = i;