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Proof step 20 from proof bitsand-cast-01 (previous step)

⊦ bits2 = [], bits2 + bits1 = [], bits0 = [], lastn(# bits1, fillsgn(# bits1, bitsand(bits1, bits0))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits0))), ¬ # bits1 < # bits0 ∧ ¬ bits0.first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ bits1.first → bitsand(bits + bits0, bits1) = bits + bitsand(bits0, bits1)
Proof step 22:
¬(# bits0 ≤ # bits1 ∧ bits0 ≠ [] ∧ bits0.first) ⊦ bits2 = [], bits2 + bits1 = [], bits0 = [], lastn(# bits1, fillsgn(# bits1, bitsand(bits1, bits0))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits0))), ¬ # bits1 < # bits0 ∧ ¬ bits0.first
Proof step 69:
# bits0 ≤ # bits1 ∧ bits0 ≠ [] ∧ bits0.first ⊦ bits2 = [], bits2 + bits1 = [], bits0 = [], lastn(# bits1, fillsgn(# bits1, bitsand(bits1, bits0))) = lastn(# bits1, fillsgn(# bits1, bits2 + bitsand(bits1, bits0))), ¬ # bits1 < # bits0 ∧ ¬ bits0.first

Rule argument

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

Additional information

Used terms: bits0, bits1, bits2