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Proof step 976 from proof bitsand-cast (previous step)

# bits = # bits1 ⊦ bits3 = [], bits1 = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits3 + bits))), bits3 + bits = [], bits2 + bits1 = [], bits1 = [], true ∈ bits1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 977:
⊦ # bits = # bits1 ∧ bits0 ≠ [] ∧ bits2 ≠ [] ∧ bits ≠ [] → bitsand(bits0 + bits, bits2 + bits1) = bitsand(bits0, bits2) + bitsand(bits, bits1)
Proof step 978:
¬(# bits1 = # bits ∧ bits2 ≠ [] ∧ bits3 ≠ [] ∧ bits1 ≠ []), # bits = # bits1 ⊦ bits3 = [], bits1 = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits3 + bits))), bits3 + bits = [], bits2 + bits1 = [], bits1 = [], true ∈ bits1
Proof step 984:
# bits1 = # bits ∧ bits2 ≠ [] ∧ bits3 ≠ [] ∧ bits1 ≠ [], # bits = # bits1 ⊦ bits3 = [], bits1 = lastn(# bits1, fillsgn(# bits1, bitsand(bits2, bits3) + bitsand(bits1, bits))), bits3 + bits = [], bits2 + bits1 = [], bits1 = [], true ∈ bits1

Rule argument

name: bitsand-app rotate: F subst: [bits1, bits2, bits, bits0] → [bits, bits3, bits1, bits2]

Additional information

Used terms: bits, bits3, bits1, bits2