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Proof step 265 from proof bitsand-cast (previous step)

n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), 2 + # bits1 = # bits, n0 < m, 2 + # bits1 + m < n0 + # bits, m ≤ # bits2 ∨ bits2.first ⊦ mklist(false, n0) = mklist(false, n0 - m) + mklist(false, m), bits2 + bits = [], bits = [], mklist(false, m) + bitsand(bits, false ' + true ' + bits1) = [], bits2 = []

User applied rule cut formula

And obtained the following new goals

Proof step 266:
m ≤ # bits2, n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), 2 + # bits1 = # bits, n0 < m, 2 + # bits1 + m < n0 + # bits, m ≤ # bits2 ∨ bits2.first ⊦ mklist(false, n0) = mklist(false, n0 - m) + mklist(false, m), bits2 + bits = [], bits = [], mklist(false, m) + bitsand(bits, false ' + true ' + bits1) = [], bits2 = []
Proof step 268:
n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), 2 + # bits1 = # bits, n0 < m, 2 + # bits1 + m < n0 + # bits, m ≤ # bits2 ∨ bits2.first ⊦ m ≤ # bits2, mklist(false, n0) = mklist(false, n0 - m) + mklist(false, m), bits2 + bits = [], bits = [], mklist(false, m) + bitsand(bits, false ' + true ' + bits1) = [], bits2 = []

Rule argument

fma: m ≤ # bits2

Additional information

Used formulas: m ≤ # bits2