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Proof step 341 from proof bitsand-cast (previous step)

# bits ≤ n ∧ bits ≠ [], n = #(mklist(bits.first, n - # bits) + bits), mklist(false, # bits) = bits, # bits0 + 1 < n, # bits < n, # bits0 < # bits, bits0.first, # bits0 < n ⊦ bits0 = [], bits = [], mklist(false, n) = mklist(bits.first, n - # bits) + bits

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 342:
mklist(false, # bits) = bits, # bits0 + 1 < n, # bits < n, # bits0 < # bits, bits0.first, # bits0 < n ⊦ bits0 = [], mklist(false, n) = mklist(bits.first, n - # bits) + bits, bits = []

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ n < m → (m - n) + n = m;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;