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Proof step 46 from proof bits2int-lasteq (previous step)

bits0 = boolvar + bits, boolvar ⊦ bits0 = [], 1 + 2 * bits2uint(bits1) = bits2int(bits0 + true ') ↔ bits2uint(bits1) = bits2int(bits0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
⊦ ~1 = bits2uint(bits1) + bits2uint(bitsinvert(bits)) ↔ bits2uint((false ' + bitsinvert(bits))+1) + bits2uint(bits1) = 0

Rule argument

Additional information

Used simplifier rules: bits2int-neg: ⊦ bits2int(true ' + bits) = ~ bits2uint(bitsinvert(true + bits) +1);%bits2uint-zeros-03: ⊦ bits2uint(false ' + bits) = bits2uint(bits);%bits2uint-one: ⊦ bits2uint(bits + true ') = bits2uint(bits) * 2 + 1;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ 2 * i = 0 ↔ i = 0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j + i = i * (j + 1);% ⊦ i * j + i * j0 = i * (j + j0);% ⊦ ~ i = j ↔ i + j = 0;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ (bits + false ')+1 = bits + true;% ⊦ bitsinvert(true ') = false ';% ⊦ bitsinvert(bits + bits0) = bitsinvert(bits) + bitsinvert(bits0);% ⊦ bitsinvert(true ' + bits) = false + bitsinvert(bits);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits ≠ [];% ⊦ boolvar + bits = boolvar ' + bits;