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Proof step 29 from proof bitsand-cast-05 (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 30:
n ≤ # bits ⊦ ∃ bits0, bits1. bits = bits0 + bits1 ∧ # bits1 = n
Proof step 31:
∃ bits0, bits2. bits = bits0 + bits2 ∧ # bits2 = 1 + # bits1, # bits1 < # bits ⊦ bits1 = [], sgn(bitsand(lastn(# bits1, bits), false ' + bits1)) = sgn(bitsand(bits, false ' + bits1)), bits = [], # bits1 = # bits

Rule argument

seq: n ≤ # bits ⊦ ∃ bits0, bits1. bits = bits0 + bits1 ∧ # bits1 = n subst: [n, bits] → [1 + # bits1, bits] rotate: F spec: list inst: bitlista name: split-rest

Additional information

Used simplifier rules: ⊦ m + 1 ≤ n ↔ m < n;% ⊦ m ≠ n → (¬ m < n ↔ n < m);% ⊦ m < n → ¬ n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: 1 + # bits1, bits