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Proof step 21 from proof bitsand-cast (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 22:
# bits0 ≤ 2 + # bits1, n = # fillsgn(n, mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1), sgn(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n0 + 1 + # bits1 < n ⊦ bits0 = [], boolvar ↔ boolvar0, n0 = 0, lastn(n, fillsgn(n, bitsand(boolvar ' + boolvar0 ' + bits1, bits0))) = lastn(n, fillsgn(n, bitsand(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1, bits0))), boolvar ∧ boolvar0
Proof step 86:
n = # fillsgn(n, mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1), sgn(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n0 + 1 + # bits1 < n ⊦ # bits0 ≤ 2 + # bits1, bits0 = [], boolvar ↔ boolvar0, n0 = 0, lastn(n, fillsgn(n, bitsand(boolvar ' + boolvar0 ' + bits1, bits0))) = lastn(n, fillsgn(n, bitsand(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1, bits0))), boolvar ∧ boolvar0

Rule argument

fma: # bits0 ≤ 2 + # bits1

Additional information

Used formulas: # bits0 ≤ 2 + # bits1