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Proof step 60 from proof bitsand-cast (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), n1] rotate: T spec: nat inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ m + 1 ≠ 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ m < n → m ≤ n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), n1