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Proof step 355 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 356:
n = # fillsgn(n, bits), # bits0 + 1 < n, # bits0 < # bits, # bits < n, # bits0 < n ⊦ bits0 = [], bits = [], mklist(false, n) = mklist(mklist(false, # bits0).first, n - # bits0) + mklist(false, # bits0), bits0.first, true ∈ bits

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n;% ⊦ # bits = 0 ↔ bits = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ n < m → (m - n) + n = m;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # mklist(boolvar, n) = n;