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Proof step 49 from proof bor-2pot-plus (previous step)

bitsinvert(int2bits(j0)) = boolvar + bits ∧ bitsinvert(int2bits(j0)) ≠ [], 0 < j, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j, boolvar, # int2bits(j0) ≤ i→n(i) ⊦ bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2int(uint2bits(j) + bitsinvert(bitsand(bitsinvert(int2bits(j0)), mklist(true, i→n(i))))) = j * 2 ^ i + j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
int2bits(j0) = false ' + bitsinvert(bits), 0 < j, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j, # int2bits(j0) ≤ i→n(i), false ∈ int2bits(j0) ⊦ bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], bits2int(uint2bits(j) + bitsinvert(bitsand(bitsinvert(int2bits(j0)), mklist(true, i→n(i))))) = j * 2 ^ i + j0

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ int2bits(j) ≠ [];% ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;%⊦ bitsinvert(bits) = true ' + bits0 ↔ bits = false ' + bitsinvert(bits0);% ⊦ boolvar + bits = boolvar ' + bits;