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Proof step 916 from proof bitsand-cast (previous step)

# bits = # bits1, mklist(true, # bits1) = bits1 ⊦ bits1 = [], bits3 + bits = [], bits = lastn(# bits1, fillsgn(# bits1, bitsand(bits3 + bits, bits1)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 917:
⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ bits1.first → bitsand(bits + bits0, bits1) = bits + bitsand(bits0, bits1)
Proof step 918:
¬(# bits1 ≤ # bits ∧ bits1 ≠ [] ∧ bits1.first), # bits = # bits1, mklist(true, # bits1) = bits1 ⊦ bits1 = [], bits3 + bits = [], bits = lastn(# bits1, fillsgn(# bits1, bitsand(bits3 + bits, bits1)))
Proof step 923:
# bits1 ≤ # bits ∧ bits1 ≠ [] ∧ bits1.first, # bits = # bits1, mklist(true, # bits1) = bits1 ⊦ bits1 = [], bits3 + bits = [], bits = lastn(# bits1, fillsgn(# bits1, bits3 + bitsand(bits, bits1)))

Rule argument

name: bitsand-app-true rotate: F subst: [bits1, bits0, bits] → [bits1, bits, bits3]

Additional information

Used terms: bits1, bits, bits3