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Proof step 95 from proof byte-law-righthift-not (previous step)

31 ≤ #(mklist(true, n) + true ') + # int2bits(~128) ∧ #(mklist(true, n) + true ') ≤ 31, 31 = # int2bits(~128) + n, i2b(bits2uint(mklist(false, n) + firstn(# int2bits(~128), int2bits(128)))) = i2b(bits2uint((mklist(true, n) + true ') + firstn(31 - #(mklist(true, n) + true '), int2bits(~128)))), 32 = n + # int2bits(128), n ≤ 32, n ≤ 31, # int2bits(~128) ≤ 32, # int2bits(128) ≤ 32 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 96:
i2b(bits2uint(mklist(false, n) + firstn(# int2bits(~128), int2bits(128)))) = i2b(bits2uint(mklist(true, n) + true ' + firstn(31 - n + 1, int2bits(~128)))), 31 = # int2bits(~128) + n, 32 = n + # int2bits(128), n ≤ 31, n ≤ 30, # int2bits(128) ≤ 32, # int2bits(~128) ≤ 32, n ≤ 32 ⊦

Rule argument

Additional information

Used simplifier rules: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward)% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)%n < n0 ⊦ m + (* n) ≤ (* n0) ↔ m ≤ n0 - n;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;%n0 < n ⊦ (* n) ≤ m0 + (* n0) ↔ n - n0 ≤ m0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;