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Proof step 63 from proof bitsand-cast (previous step)

sgn(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n = # fillsgn(n, mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1), # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n, # bits0 ≤ 2 + # bits1, bits0.first, n0 + 1 + # bits1 < n, (n0 - 1) + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n, n0 + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) ≤ n + 1 ⊦ (mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)).first ↔ boolvar, mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0) = [], n0 = 0, boolvar ↔ boolvar0, bits0 = [], mklist(boolvar, n - # bitsand(boolvar ' + boolvar0 ' + bits1, bits0)) = mklist ((mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)).first, n - (n0 - 1) + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0)) + mklist(boolvar, n0 - 1), boolvar ∧ boolvar0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 64:
n0 = m + 1, sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n = # fillsgn(n, mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits1), # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n, # bits0 ≤ 2 + # bits1, bits0.first, n0 + 1 + # bits1 < n, m + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) < n, n0 + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) ≤ n + 1 ⊦ (mklist(boolvar, m) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)).first ↔ boolvar, mklist(boolvar, m) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0) = [], n0 = 0, boolvar ↔ boolvar0, bits0 = [], mklist(boolvar, n - # bitsand(boolvar ' + boolvar0 ' + bits1, bits0)) = mklist((mklist(boolvar, m) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)).first, n - m + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0)) + mklist(boolvar, m), boolvar ∧ boolvar0

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