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Proof step 87 from proof bitsand-cast (previous step)

sgn(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n = # fillsgn(n, mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1), 2 + # bits1 < # bits0, n0 + 1 + # bits1 < n ⊦ lastn(n, fillsgn(n, bitsand(boolvar ' + boolvar0 ' + bits1, bits0))) = lastn(n, fillsgn(n, bitsand(mklist(boolvar, n0 - 1) + boolvar ' + boolvar0 ' + bits1, bits0))), n0 = 0, boolvar ↔ boolvar0, bits0 = [], boolvar ∧ boolvar0

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: n ≤ # bits ⊦ ∃ bits0, bits1. bits = bits0 + bits1 ∧ # bits1 = n subst: [n, bits] → [2 + # bits1, 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 + # bits1, bits0