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Proof step 156 from proof bitsand-cast (previous step)

n = # fillsgn(n, fillsgn(m, 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 ≤ n ⊦ bits2 + bitsand(bits, true ' + false ' + bits1) = [], bits2 = [], bits = [], bits2 + bits = [], mklist(true, n - # bits2 + # bits) + bits2 + bitsand(bits, true ' + false ' + bits1) = fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1))

User applied rule insert elim lemma

And obtained the following new goals

Proof step 157:
n = n0 + # bits2 + # bits, n = # fillsgn(n, fillsgn(m, 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 ≤ n ⊦ bits2 + bitsand(bits, true ' + false ' + bits1) = [], bits2 = [], bits = [], bits2 + bits = [], mklist(true, n0) + bits2 + bitsand(bits, true ' + false ' + bits1) = fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1))

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, # bits2 + # bits, n0] rotate: T spec: nat inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ m + n = n + m;%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, # bits2 + # bits, n0