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Proof step 421 from proof bitsand-cast (previous step)

# bits1 = 2 + # bits, sgn(mklist(true, m) + true ' + false ' + bits) = true ' + false ' + bits, bits3.first, # bits3 ≤ m ⊦ bits1 = [], bits3 + bits1 = [], bits3 = [], bits2 + mklist(true, m) = [], lastn(2 + # bits + m, fillsgn(2 + # bits + m, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bits2 + mklist(true, m - # bits3) + bits3 + bitsand(bits1, true ' + false ' + bits)))

User applied rule insert elim lemma

And obtained the following new goals

Proof step 422:
m = n + # bits3, # bits1 = 2 + # bits, sgn(mklist(true, m) + true ' + false ' + bits) = true ' + false ' + bits, bits3.first, # bits3 ≤ m ⊦ bits1 = [], bits3 + bits1 = [], bits3 = [], bits2 + mklist(true, m) = [], lastn(2 + # bits + m, fillsgn(2 + # bits + m, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bits2 + mklist(true, n) + bits3 + bitsand(bits1, true ' + false ' + bits)))

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [m, # bits3, n] rotate: T spec: nat inst: name: elim-sub

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m, # bits3, n