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Proof step 136 from proof bitsand-cast (previous step)

n ≠ # fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)), n = # fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)), # bits = 2 + # bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, bits2.first, # bits2 < m, 2 + # bits1 + m < n ⊦ bits2 = [], bits = [], bits2 + bits = [], fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)) = lastn(n, fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 137:
sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), # bits = 2 + # bits1, n = # fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)), 2 + # bits1 + m < n, # bits2 < m, bits2.first ⊦ n = # fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)), fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)) = lastn(n, fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1))), bits2 + bits = [], bits = [], bits2 = []

Rule argument

Additional information

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