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Proof step 58 from proof bor-2pot-plus (previous step)

¬ false ∈ mklist(true, i→n(i)) ∧ # bitsinvert(int2bits(j0)) ≤ # mklist(true, i→n(i)) ∧ bitsinvert(int2bits(j0)).first ∧ bitsinvert(int2bits(j0)) ≠ [], 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)) = [], bits2uint(bitsinvert(fillsgn(# mklist(true, i→n(i)), bitsinvert(int2bits(j0))))) + 2 ^ n→i(# fillsgn(# mklist(true, i→n(i)), bitsinvert(int2bits(j0)))) * j = j * 2 ^ i + j0, fillsgn(# mklist(true, i→n(i)), bitsinvert(int2bits(j0))) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
int2bits(j0) = false ' + bitsinvert(bits), 0 < j, j0 < 2 ^ i, 0 ≤ i, 0 ≤ j0, 0 < 2 ^ i, 0 ≤ j, false ∈ int2bits(j0), # int2bits(j0) ≤ i→n(i) ⊦ bitsinvert(uint2bits(j)) + mklist(true, i→n(i)) = [], 2 ^ n→i(# fillsgn(i→n(i), bitsinvert(int2bits(j0)))) * j + bits2uint(bitsinvert(fillsgn(i→n(i), bitsinvert(int2bits(j0))))) = j * 2 ^ i + j0, fillsgn(i→n(i), bitsinvert(int2bits(j0))) = []

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ false ∈ mklist(true, n);% ⊦ 0 ≤ j → bitsinvert(int2bits(j)).first;% ⊦ # bitsinvert(bits) = # bits;% ⊦ int2bits(j) ≠ [];% ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ # mklist(boolvar, n) = n;