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Proof step 40 from proof bitsand-cast-04 (previous step)

# bits1 ≤ # bits0 + n0, # bits0 < # bits1 ⊦ sgn(bitsand(mklist(false, n0) + false ' + bits0, false ' + bits1)) = sgn(bitsand(bits1, false ' + bits0)), n0 = 0, bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ ¬ true ∈ bits → sgn(bitsand(bits + false ' + bits0, false ' + bits1)) = sgn(bitsand(false ' + bits0, false ' + bits1))
Proof step 42:
¬ true ∈ mklist(false, n0), # bits1 ≤ # bits0 + n0, # bits0 < # bits1 ⊦ sgn(bitsand(false ' + bits0, false ' + bits1)) = sgn(bitsand(bits1, false ' + bits0)), n0 = 0, bits1 = []

Rule argument

name: bitsand-app-zeros rotate: F subst: [bits1, bits0, bits] → [bits1, bits0, mklist(false, n0)]

Additional information

Used simplifier rules: ⊦ ¬ true ∈ mklist(false, n); Used terms: bits1, bits0, mklist(false, n0)