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Proof step 84 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [ mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0), n] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used simplifier rules: ⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # mklist(boolvar, n) = n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ ¬ m + n < m; Used terms: mklist(boolvar, n0 - 1) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0), n