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Proof step 932 from proof bitsand-cast (previous step)

# bits = # bits1, mklist(true, # bits1) = bits1 ⊦ bits2 = [], bits1 = [], bits2 + bits1 = [], bits = [], bits = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 933:
⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ ¬ bits1.first → bitsand(bits + bits0, bits1) = bitsand(bits0, bits1)
Proof step 934:
¬(# bits ≤ # bits1 ∧ bits ≠ [] ∧ ¬ bits.first), # bits = # bits1, mklist(true, # bits1) = bits1 ⊦ bits2 = [], bits1 = [], bits2 + bits1 = [], bits = [], bits = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits)))
Proof step 942:
# bits ≤ # bits1 ∧ bits ≠ [] ∧ ¬ bits.first, # bits = # bits1, mklist(true, # bits1) = bits1 ⊦ bits2 = [], bits1 = [], bits2 + bits1 = [], bits = [], bits = lastn(# bits1, fillsgn(# bits1, bitsand(bits1, bits)))

Rule argument

name: bitsand-app-false rotate: F subst: [bits1, bits0, bits] → [bits, bits1, bits2]

Additional information

Used terms: bits, bits1, bits2