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Proof step 432 from proof bitsand-cast (previous step)

sgn((mklist(true, n) + mklist(true, # bits3)) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, # bits1 ≤ 2 + # bits + n, bits3.first ⊦ lastn(2 + # bits + n + # bits3, mklist(true, 2 + # bits + n - # bits1) + bits3 + bitsand(bits1, true ' + false ' + bits)) = lastn(2 + # bits + n + # bits3, fillsgn(2 + # bits + n + # bits3, bits2 + mklist(true, n) + bits3 + bitsand(bits1, true ' + false ' + bits))), bits3 + bitsand(bits1, true ' + false ' + bits) = [], bits2 + mklist(true, n) + mklist(true, # bits3) = [], bits3 = [], bits3 + bits1 = [], bits1 = []

User applied rule insert elim lemma

And obtained the following new goals

Proof step 433:
2 + # bits + n = n0 + # bits1, sgn((mklist(true, n) + mklist(true, # bits3)) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, # bits1 ≤ 2 + # bits + n, bits3.first ⊦ lastn(2 + # bits + n + # bits3, mklist(true, n0) + bits3 + bitsand(bits1, true ' + false ' + bits)) = lastn(2 + # bits + n + # bits3, fillsgn(2 + # bits + n + # bits3, bits2 + mklist(true, n) + bits3 + bitsand(bits1, true ' + false ' + bits))), bits3 + bitsand(bits1, true ' + false ' + bits) = [], bits2 + mklist(true, n) + mklist(true, # bits3) = [], bits3 = [], bits3 + bits1 = [], bits1 = []

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [2 + # bits + n, # bits1, n0] rotate: T spec: nat inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: 2 + # bits + n, # bits1, n0