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Proof step 702 from proof bitsand-cast (previous step)

# bits1 = 2 + # bits, # bits3 < m ⊦ mklist(false, m) = mklist(false, m - # bits3) + mklist(false, # bits3), bits2 + mklist(false, m) = [], bits3 + bits1 = [], bits3 = [], bits1 = [], mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits) = [], # bits3 = m, bits3.first

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] → [m, # bits3, 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: m, # bits3, n