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Proof step 110 from proof bitsand-cast (previous step)

sgn(mklist(true, n0 - 1) + true ' + false ' + bits1) = true ' + false ' + bits1, n = # fillsgn(n, mklist(true, n0 - 1) + true ' + false ' + bits1), # bits = 2 + # bits1, n0 + 1 + # bits1 < n ⊦ bits2 = [], lastn(n, fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1))) = lastn(n, fillsgn(n, bitsand(bits2, mklist(true, n0 - 1)) + bitsand(bits, true ' + false ' + bits1))), n0 = 0, bits2 + bits = [], bits = [], n0 - 1 = 0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 111:
n0 = m + 1, sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), # bits = 2 + # bits1, n0 + 1 + # bits1 < n ⊦ bits2 = [], lastn(n, fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1))) = lastn(n, fillsgn(n, bitsand(bits2, mklist(true, m)) + bitsand(bits, true ' + false ' + bits1))), n0 = 0, bits2 + bits = [], bits = [], m = 0

Rule argument

seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n0, 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: n0, m