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Proof step 25 from proof bitsand-cast-01 (previous step)

# bits1 < # bits0 ⊦ lastn(# bits1, fillsgn(# bits1, bitsand(bits1, bits0))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits0))), bits0 = [], bits2 + bits1 = [], bits2 = []

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 26:
n ≤ # bits ⊦ ∃ bits0, bits1. bits = bits0 + bits1 ∧ # bits1 = n
Proof step 27:
∃ bits3, bits2. bits0 = bits3 + bits2 ∧ # bits2 = # bits1, # bits1 < # bits0 ⊦ lastn(# bits1, fillsgn(# bits1, bitsand(bits1, bits0))) = lastn(# bits1, fillsgn(# bits1, bitsand(bits2 + bits1, bits0))), bits0 = [], bits2 + bits1 = [], bits2 = []

Rule argument

seq: n ≤ # bits ⊦ ∃ bits0, bits1. bits = bits0 + bits1 ∧ # bits1 = n subst: [n, bits] → [# bits1, bits0] rotate: F spec: list inst: bitlista name: split-rest

Additional information

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