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Proof step 454 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 455:
# bits1 = 2 + # bits, sgn((mklist(true, n) + mklist(true, # bits3)) + true ' + false ' + bits) = true ' + false ' + bits, 2 + # bits + n = n0 + # bits1, bits3.first, # bitsand(bits1, true ' + false ' + bits) ≤ n0 + # bits1 ⊦ bits1 = [], bits3 + bits1 = [], bits3 = [], bits2 + mklist(true, n) + mklist(true, # bits3) = [], bits3 + bitsand(bits1, true ' + false ' + bits) = [], mklist(true, n0) = lastn(n0 + # bits1 - # bitsand(bits1, true ' + false ' + bits), mklist(true, n))

Rule argument

Additional information

Used simplifier rules: ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ bits + bits0 = bits1 + bits0 ↔ bits = bits1;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n - n + n1 = m - n1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;