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Proof step 280 from proof bitsand-cast (previous step)

n = # fillsgn(n, bits), mklist(true, # bits) = bits, true ∈ bits, # bits < n ⊦ bits = [], bits0 = [], lastn(n, fillsgn(n, bits0)) = lastn(n, fillsgn(n, bitsand(bits, bits0))), ¬ false ∈ bits ∧ ¬ # bits < # bits0 ∧ bits0.first, ¬ false ∈ bits ∧ ¬ # bits0 < # bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 281:
⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ ¬ bits0.first ∧ bits0 ≠ [] → bitsand(bits, bits0) = bits0
Proof step 282:
¬(¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ ¬ bits0.first ∧ bits0 ≠ []), n = # fillsgn(n, bits), mklist(true, # bits) = bits, true ∈ bits, # bits < n ⊦ bits = [], bits0 = [], lastn(n, fillsgn(n, bits0)) = lastn(n, fillsgn(n, bitsand(bits, bits0))), ¬ false ∈ bits ∧ ¬ # bits < # bits0 ∧ bits0.first, ¬ false ∈ bits ∧ ¬ # bits0 < # bits

Rule argument

name: add-ones-grlen-02 rotate: F subst: [bits0, bits] → [bits0, bits]

Additional information

Used terms: bits0, bits