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Proof step 55 from proof bitsand-cast-04 (previous step)

# bits0 = 1 + # bits1, # bits1 < n, # bits1 < # bits0, n ≤ # bits2 + # bits0, # bits1 < # bits2 + # bits0, # bits0 ≤ n ⊦ sgn(bitsand(lastn(n, bits2 + bits0), false ' + bits1)) = sgn(bitsand(bits0, false ' + bits1)), bits2 + bits0 = [], bits0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 56:
⊦ # bits ≤ n → lastn(n, bits0 + bits) = lastn(n - # bits, bits0) + bits
Proof step 57:
# bits0 ≤ n, # bits0 = 1 + # bits1, # bits1 < n, # bits1 < # bits0, n ≤ # bits2 + # bits0, # bits1 < # bits2 + # bits0, # bits0 ≤ n ⊦ sgn(bitsand(lastn(n - # bits0, bits2) + bits0, false ' + bits1)) = sgn(bitsand(bits0, false ' + bits1)), bits2 + bits0 = [], bits0 = []

Rule argument

seq: ⊦ # bits ≤ n → lastn(n, bits0 + bits) = lastn(n - # bits, bits0) + bits subst: [bits, bits0, n] → [bits0, bits2, n] rotate: F spec: list-del inst: bitlista name: lastn-app

Additional information

Used terms: bits0, bits2, n