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Proof step 406 from proof bitsand-cast (previous step)

sgn(mklist(true, n - 1) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits ⊦ lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits3, bits2 + mklist(true, n - 1)) + bitsand(bits1, true ' + false ' + bits))), n = 0, bits3 + bits1 = [], bits1 = [], bits2 + mklist(true, n - 1) = [], bits3 = []

User applied rule insert elim lemma

And obtained the following new goals

Proof step 407:
n = m + 1, sgn(mklist(true, m) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits ⊦ lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits3, bits2 + mklist(true, m)) + bitsand(bits1, true ' + false ' + bits))), n = 0, bits3 + bits1 = [], bits1 = [], bits2 + mklist(true, m) = [], bits3 = []

Rule argument

seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m] rotate: T spec: nat inst: name: elim-pred-c

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m