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Proof step 35 from proof bitsand-cast-05 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits)
Proof step 37:
# bits1 ≤ # bits0, # bits0 = 1 + # bits1, # bits1 < # bits0, # bits1 < # bits2 + # bits0 ⊦ bits1 = [], sgn(bitsand(lastn(# bits1, bits0), false ' + bits1)) = sgn(bitsand(bits0, false ' + bits1)), bits2 + bits0 = [], # bits1 = # bits2 + # bits0, bits0 = []

Rule argument

seq: ⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits) subst: [bits, bits0, n] → [bits0, bits2, # bits1] rotate: F spec: list-del inst: bitlista name: lastN-append-01

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m; Used terms: bits0, bits2, # bits1