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Proof step 451 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, mklist(true, n) + bits3 + bitsand(bits1, true ' + false ' + bits))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 452:
2 + # bits + n = n0 + # bits1, sgn((mklist(true, n) + mklist(true, # bits3)) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, n0 + # bits1 < # bitsand(bits1, true ' + false ' + bits), bits3.first ⊦ mklist(true, n0) + bits3 + bitsand(bits1, true ' + false ' + bits) = lastn(2 + # bits + n + # bits3, 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

Additional information

Used simplifier rules: and-notempty-01: ⊦ bits ≠ [] → bitsand(bits, boolvar ' + bits0) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;