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Proof step 385 from proof bitsand-cast (previous step)

sgn(mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits, 2 + # bits < # bits0 ⊦ lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(boolvar, n - 1)) + boolvar ' + boolvar0 ' + bits, bits0))), n = 0, bits0 = [], boolvar ↔ boolvar0, boolvar ∧ boolvar0

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 386:
n ≤ # bits ⊦ ∃ bits0, bits1. bits = bits0 + bits1 ∧ # bits1 = n
Proof step 387:
∃ bits2, bits1. bits0 = bits2 + bits1 ∧ # bits1 = 2 + # bits, sgn(mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits, 2 + # bits < # bits0 ⊦ lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(boolvar, n - 1)) + boolvar ' + boolvar0 ' + bits, bits0))), n = 0, bits0 = [], boolvar ↔ boolvar0, boolvar ∧ boolvar0

Rule argument

seq: n ≤ # bits ⊦ ∃ bits0, bits1. bits = bits0 + bits1 ∧ # bits1 = n subst: [n, bits] → [2 + # bits, bits0] rotate: F spec: list inst: bitlista name: split-rest

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m + n = n + m;% ⊦ m < n → ¬ n < m; Used terms: 2 + # bits, bits0