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Proof step 8 from proof bits2int-range (previous step)

bits = boolvar + bits0, # bits = m + 1, boolvar ⊦ bits = [], ¬ 2 ^ n→i(m) + bits2int(bits) < 0 ∧ ¬ 2 ^ n→i(m) ≤ bits2int(bits)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
⊦ ¬ 2 ^ n→i(# bits0) < bits2uint((false ' + bitsinvert(bits0))+1) ∧ ¬ 2 ^ n→i(# bits0) + bits2uint((false ' + bitsinvert(bits0))+1) ≤ 0

Rule argument

Additional information

Used simplifier rules: bits2int-neg: ⊦ bits2int(true ' + bits) = ~ bits2uint(bitsinvert(true + bits) +1);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ ~ j ↔ i + j ≤ 0;% ⊦ i + 0 = i;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + ~ j = i - j;% ⊦ bitsinvert(true ' + bits) = false + bitsinvert(bits);% ⊦ boolvar ' + bits ≠ [];% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ boolvar + bits = boolvar ' + bits;