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Proof step 311 from proof bitsand-cast (previous step)

n1 = n + n0 ∧ n0 ≤ n1, n1 + # bits0 = # fillsgn(n1 + # bits0, bits), # bits = n0 + # bits0, n0 < n1, true ∈ bits, bits0.first, # bits0 ≤ # bits, # bits < n1 + # bits0 ⊦ n0 = 0, mklist(true, n0) + bits0 = [], bits = [], bits0 = [], mklist(true, n1) + bits0 = lastn(n1 + # bits0, mklist(true, n) + mklist(true, n0) + bits0), false ∈ bits

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 312:
# bits = n0 + # bits0, (n + n0) + # bits0 = # fillsgn((n + n0) + # bits0, bits), # bits0 ≤ # bits, bits0.first, true ∈ bits, # bits < (n + n0) + # bits0 ⊦ n = 0, (mklist(true, n) + mklist(true, n0)) + bits0 = lastn((n + n0) + # bits0, mklist(true, n) + mklist(true, n0) + bits0), bits0 = [], bits = [], mklist(true, n0) + bits0 = [], n0 = 0, n + n0 = 0, false ∈ bits

Rule argument

Additional information

Used simplifier rules: ⊦ m + n < m + n0 ↔ n < n0;% ⊦ m < n → n ≠ 0;% ⊦ m ≤ n ∧ n < n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < m + n ↔ n ≠ 0;% ⊦ m < n → m ≤ n;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);