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Proof step 37 from proof bitsand-cast-05 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
# bits0 = 1 + # bits1, # bits1 < # bits0, # bits1 < # bits2 + # bits0 ⊦ bits2 + bits0 = [], # bits1 = # bits2 + # bits0, bits0 = [], bits1 = [], sgn(bitsand(bits0.rest, false ' + bits1)) = sgn(bitsand(bits0, false ' + bits1))

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n;% ⊦ # bits = n + 1 → lastn(n, bits) = bits.rest;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;