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Proof step 51 from proof bitsand-cast-04 (previous step)

∃ bits0, bits2. bits = bits0 + bits2 ∧ # bits2 = 1 + # bits1, n ≤ # bits, # bits1 < n, # bits1 < # bits ⊦ sgn(bitsand(lastn(n, bits), false ' + bits1)) = sgn(bitsand(bits, false ' + bits1)), bits = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
# bits0 = 1 + # bits1, # bits0 ≤ n, # bits1 < # bits2 + # bits0, # bits1 < n, n ≤ # bits2 + # bits0 ⊦ bits2 + bits0 = [], sgn(bitsand(lastn(n, bits2 + bits0), false ' + bits1)) = sgn(bitsand(bits2 + bits0, false ' + bits1))

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n;% ⊦ m < n → n ≠ 0;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m = n + 1 ∧ n < n0 → m ≤ n0; (forward)% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;