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Proof step 32 from proof bor-2pot-plus (previous step)

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

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n → ¬ n < m;