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Proof step 105 from proof byte-law-righthift-not (previous step)

~128 < 0, 31 = # sgn(bitsinvert(uint2bits(abs(~128))) +1) + n, 32 = n + # int2bits(128), 30 = n0 + n, i2b(bits2uint(firstn(# sgn(bitsinvert(uint2bits(abs(~128))) +1), int2bits(128)))) = i2b(bits2uint(true ' + firstn(n0, sgn(bitsinvert(uint2bits(abs(~128))) +1))) + 2 ^ (1 + n→i(n0)) * bits2uint(mklist(true, n))), n ≤ 31, # int2bits(128) ≤ 32, # sgn(bitsinvert(uint2bits(abs(~128))) +1) ≤ 32, n ≤ 32, n ≤ 30 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ 0 ≤ j ∧ 1 < n → (# int2bits(j) = n ↔ 2 ^ (n→i(n) - 2) ≤ j ∧ j < 2 ^ (n→i(n) - 1));% ⊦ bits2uint(true ') = 1;% ⊦ bits2uint(bits + true ') = bits2uint(bits) * 2 + 1;% ⊦ bits + [] = bits;% ⊦ mklist(boolvar, 0) = [];%n ≠ 0 ⊦ mklist(true, (* n)) = true ' + mklist(true, n -1);% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;%n0 < n ⊦ (* n) = m0 + (* n0) ↔ n - n0 = m0;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ sgn(true ' + false ' + bits) = true ' + false ' + bits;% ⊦ sgn(boolvar ' + boolvar ' + bits) = sgn(boolvar ' + bits);% ⊦ (bits + false ')+1 = bits + true;% ⊦ (bits + true ')+1 = bits +1 + false;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ bitsinvert(false ') = true ';% ⊦ bitsinvert(true ' + bits) = false + bitsinvert(bits);% ⊦ bitsinvert(false ' + bits) = true + bitsinvert(bits);% ⊦ bits + boolvar = bits + boolvar ';% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ uint2bits(1) = false + true;%1 < i ⊦ uint2bits((* i)) = uint2bits(i / 2) + (i % 2 = 1);