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Proof step 112 from proof bitsand-cast (previous step)

sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), # bits = 2 + # bits1, 2 + # bits1 + m < n ⊦ bits2 = [], lastn(n, fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1))) = lastn(n, fillsgn(n, bitsand(bits2, mklist(true, m)) + bitsand(bits, true ' + false ' + bits1))), bits2 + bits = [], bits = [], m = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 113:
⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits)
Proof step 114:
bits2 ≠ [] ∧ mklist(true, m) ≠ [], sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), # bits = 2 + # bits1, 2 + # bits1 + m < n ⊦ bits2 = [], lastn(n, fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1))) = lastn(n, fillsgn(n, bitsand(mklist(true, m), bits2) + bitsand(bits, true ' + false ' + bits1))), bits2 + bits = [], bits = [], m = 0

Rule argument

name: and-com rotate: F subst: [bits0, bits] → [mklist(true, m), bits2]

Additional information

Used simplifier rules: ⊦ mklist(boolvar, m) = [] ↔ m = 0; Used terms: mklist(true, m), bits2