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Proof step 172 from proof bitsand-cast (previous step)

sgn((mklist(true, n) + mklist(true, # bits2)) + true ' + false ' + bits1) = true ' + false ' + bits1, n0 + # bits2 + # bits = # fillsgn(n0 + # bits2 + # bits, (mklist(true, n) + mklist(true, # bits2)) + true ' + false ' + bits1), # bits = 2 + # bits1, n ≤ n0, 2 + # bits1 + n < n0 + # bits, bits2.first ⊦ mklist(true, n0) = mklist(true, n0 - n) + mklist(true, n), mklist(true, n) + bits2 + bitsand(bits, true ' + false ' + bits1) = [], n = 0, bits2 + bits = [], bits = [], bits2 + bitsand(bits, true ' + false ' + bits1) = [], bits2 = []

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, n, n1] 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, n, n1