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Proof step 835 from proof bitsand-cast (previous step)

sgn(mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits, bits0.first, # bits0 ≤ 2 + # bits ⊦ boolvar ↔ boolvar0, n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, (bits2 + mklist(boolvar, n - 1)) + bitsand(boolvar ' + boolvar0 ' + bits, bits0))), bits0 = [], boolvar ∧ boolvar0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 836:
n = m + 1, sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits, bits0.first, # bits0 ≤ 2 + # bits ⊦ boolvar ↔ boolvar0, n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, (bits2 + mklist(boolvar, m)) + bitsand(boolvar ' + boolvar0 ' + bits, bits0))), bits0 = [], boolvar ∧ boolvar0

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