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Proof step 80 from proof bits2int-pos (previous step)

# bits0 ≤ 7 ⊦ ¬ 127 < bits2int(boolvar ' + bits0), 0 ≤ b2i(i2b(bits2int(boolvar ' + bits0))) ↔ ¬ boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 81:
0 < bits2uint(bits0), b2i(i2b(bits2uint(bits0))) < 0, 127 < bits2uint(bits0), # bits0 ≤ 7 ⊦

Rule argument

Additional information

Used simplifier rules: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j;% ⊦ bits2int(false ' + bits) = bits2uint(bits);% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ¬ bits2uint(bits) < 0;% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ i < ~ j ↔ i + j < 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bitsinvert(true ' + bits) = false + bitsinvert(bits);% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ bits2int(true ' + bits) = ~ bits2uint(bitsinvert(true + bits) +1);