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Proof step 12 from proof at-range (previous step)

n < # zbrar, n < nused, n + 1 < nused, key ∈ (ri |> zbrar[n - 1].key) |≤ zbrar[n].key, nused ≤ # zbrar ⊦ ((ri |> zbrar[n - 1].key) |≤ zbrar[n].key)[key] = ri[key], n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
n + 1 < nused, n < nused, n < # zbrar, zbrar[n - 1].key < key, n + 1 < # zbrar, key ∈ ri, nused ≤ # zbrar ⊦ ((ri |> zbrar[n - 1].key) |≤ zbrar[n].key)[key] = ri[key], n = 0, zbrar[n].key < key

Rule argument

Additional information

Used simplifier rules: fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ key0 ∈ ri |> key1 ↔ key0 ∈ ri ∧ key1 < key0; (s)% ⊦ key0 ∈ ri |≤ key1 ↔ key0 ∈ ri ∧ ¬ key1 < key0; (s)