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Proof step 55 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) = [], 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 cut formula

And obtained the following new goals

Proof step 56:
(mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)).first ↔ boolvar, 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) = [], 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
Proof step 63:
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

Rule argument

fma: ( mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0) ).first ↔ boolvar

Additional information

Used formulas: ( mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0) ).first ↔ boolvar