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Proof step 252 from proof bitsand-cast (previous step)

n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), 2 + # bits1 = # bits, # bits2 < m, 2 + # bits1 + m < n0 + # bits, # bits2 ≤ n0 ⊦ bits2 + bits = [], bits = [], bits2 = [], mklist(false, # bits2) + bitsand(bits, false ' + true ' + bits1) = [], mklist(false, n0) = mklist(false, n0 - # bits2) + mklist(false, # bits2), bits2.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] → [n0, # bits2, n] rotate: T spec: nat inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ 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: n0, # bits2, n