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Proof step 335 from proof bitsand-cast (previous step)

n = # fillsgn(n, bits), # bits < n, # bits ≤ # bits0 ∨ bits0.first ⊦ # bits ≤ # bits0, bits0 = [], bits = [], mklist(false, n) = fillsgn(n, bits), true ∈ bits, ¬ # bits ≤ # bits0 ∧ ¬ bits0.first

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 336:
n = # fillsgn(n, bits), # bits0 + 1 < n, # bits < n, # bits0 < # bits, bits0.first, # bits0 < n ⊦ bits0 = [], bits = [], mklist(false, n) = fillsgn(n, bits), true ∈ bits

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m +1 = m + 1;% ⊦ # bits = 0 ↔ bits = [];% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ m < n → (n ≤ m ↔ false);% ⊦ ¬ m ≤ n ↔ n < m;