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Proof step 975 from proof bitsand-cast (previous step)

∃ bits3, bits2. bits0 = bits3 + bits2 ∧ # bits2 = # bits1, # bits1 < # bits0 ⊦ bits1 = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits0))), bits0 = [], bits2 + bits1 = [], bits1 = [], true ∈ bits1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 976:
# bits = # bits1 ⊦ bits3 = [], bits1 = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits3 + bits))), bits3 + bits = [], bits2 + bits1 = [], bits1 = [], true ∈ bits1

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < m + n ↔ n ≠ 0;% ⊦ m < n → n ≠ 0;% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;