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Proof step 42 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

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