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Proof step 274 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)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 275:
⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ bits0.first ∧ bits0 ≠ [] → bitsand(bits, bits0) = fillsgn(# bits, bits0)
Proof step 276:
¬(¬ 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)))
Proof step 286:
¬ 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, fillsgn(# bits, bits0)))

Rule argument

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

Additional information

Used terms: bits0, bits