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Proof step 21 from proof bits2int-split-01 (previous step)

false ' + bitsinvert(bits1) ≠ [] ⊦ bits0 = [], (bits2uint(false ' + bitsinvert(bits1)) + 1) * 2 ^ n→i(# bits0) = (bits2uint(bitsinvert(bits1)) * 2 ^ n→i(# bits0) + bits2uint(bitsinvert(bits0))) + 1, true ∈ bits0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
⊦ bits0 = [], 2 ^ n→i(# bits0) = bits2uint(bitsinvert(bits0)) + 1, true ∈ bits0

Rule argument

Additional information

Used simplifier rules: bits2uint-zeros-03: ⊦ bits2uint(false ' + bits) = bits2uint(bits);% ⊦ boolvar ' + bits ≠ [];% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 1 * i = i;% ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = j0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;