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Proof step 62 from proof bitsand-cast (previous step)

(mklist(boolvar, m) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0)).first ↔ boolvar, sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits1) = boolvar ' + boolvar0 ' + bits1, n1 + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) = # fillsgn(n1 + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0), mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits1), # bits0 ≤ 2 + # bits1, bits0.first, m < n1, 2 + # bits1 + m < n1 + # bitsand(boolvar ' + boolvar0 ' + bits1, bits0) ⊦ mklist(boolvar, m) + bitsand(boolvar ' + boolvar0 ' + bits1, bits0) = [], boolvar ↔ boolvar0, bits0 = [], mklist(boolvar, n1) = mklist(boolvar, n1 - m) + mklist(boolvar, m), boolvar ∧ boolvar0

User applied rule insert elim lemma

And closed the goal!

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n1, m, n] rotate: T spec: nat inst: name: elim-sub

Additional information

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