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Proof step 22 from proof bitsand-cast (previous step)

# 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ ¬ bits1.first → bitsand(bits + bits0, bits1) = bitsand(bits0, bits1)
Proof step 24:
¬(# bits0 ≤ #(boolvar ' + boolvar0 ' + bits1) ∧ bits0 ≠ [] ∧ ¬ bits0.first), # 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

Rule argument

name: bitsand-app-false rotate: F subst: [bits1, bits0, bits] → [bits0, boolvar ' + boolvar0 ' + bits1, mklist(boolvar, n0 - 1)]

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bits0, boolvar ' + boolvar0 ' + bits1, mklist(boolvar, n0 - 1)