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Proof step 303 from proof bitsand-cast (previous step)

#(mklist(true, n0) + bits0) ≤ n1 + # bits0 ∧ mklist(true, n0) + bits0 ≠ [], n1 + # bits0 = # fillsgn(n1 + # bits0, bits), # bits = n0 + # bits0, n0 < n1, true ∈ bits, bits0.first, # bits0 ≤ # bits, # bits < n1 + # bits0 ⊦ bits = [], bits0 = [], mklist(true, n1) + bits0 = lastn(n1 + # bits0, mklist((mklist(true, n0) + bits0).first, n1 + # bits0 - #(mklist(true, n0) + bits0)) + mklist(true, n0) + bits0), false ∈ bits

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 304:
n1 + # bits0 = # fillsgn(n1 + # bits0, bits), # bits = n0 + # bits0, n0 < n1, true ∈ bits, bits0.first, # bits0 ≤ # bits, # bits < n1 + # bits0 ⊦ mklist(true, n0) + bits0 = [], bits = [], bits0 = [], mklist(true, n1) + bits0 = lastn(n1 + # bits0, mklist((mklist(true, n0) + bits0).first, n1 - n0) + mklist(true, n0) + bits0), false ∈ bits

Rule argument

Additional information

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