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Proof step 19 from proof lastn-fill-sgn (previous step)

# bits0 = # fillsgn(# bits0, sgn(bits1 + bits0)), # sgn(bits1 + bits0) + 1 < # bits1 + # bits0, # sgn(bits1 + bits0) < # bits0, # sgn(bits1 + bits0) < # bits1 + # bits0 ⊦ bits1 = [], bits1 + bits0 = [], fillsgn(# bits0, sgn(bits1 + bits0)) = lastn(# bits0, bits1 + bits0), bits0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ n = # bits → lastn(n, bits0 + bits) = bits
Proof step 21:
# bits0 = # bits0, # bits0 = # fillsgn(# bits0, sgn(bits1 + bits0)), # sgn(bits1 + bits0) + 1 < # bits1 + # bits0, # sgn(bits1 + bits0) < # bits0, # sgn(bits1 + bits0) < # bits1 + # bits0 ⊦ bits1 = [], bits1 + bits0 = [], fillsgn(# bits0, sgn(bits1 + bits0)) = bits0, bits0 = []

Rule argument

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

Additional information

Used terms: bits0, bits1, # bits0