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Proof step 27 from proof range-put (previous step)

n = m + 1, n + 1 < # zbrar, zbrar[m].key < key, n < nused, n < # zbrar, n + 1 < nused, nused ≤ # zbrar ⊦ n = 0, zbrar[n].key < key, (key0 = key ∨ key0 ∈ ri ∧ zbrar[m].key < key0 ∧ ¬ zbrar[n].key < key0 → key0 ∈ ((ri |> zbrar[m].key) |≤ zbrar[n].key)[key, adr]) ∧ (key0 ∈ ((ri |> zbrar[m].key) |≤ zbrar[n].key)[key, adr] → ri[key, adr][key0] = ((ri |> zbrar[m].key) |≤ zbrar[n].key)[key, adr][key0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
2 + m < nused, m + 1 < nused, zbrar[m].key < key, 2 + m < # zbrar, m + 1 < # zbrar, nused ≤ # zbrar ⊦ zbrar[m + 1].key < key, (key0 = key ∨ key0 ∈ ri ∧ zbrar[m].key < key0 ∧ ¬ zbrar[m + 1].key < key0 → key0 ∈ ((ri |> zbrar[m].key) |≤ zbrar[m + 1].key)[key, adr]) ∧ ( key0 ∈ ((ri |> zbrar[m].key) |≤ zbrar[m + 1].key)[key, adr] → ri[key, adr][key0] = ((ri |> zbrar[m].key) |≤ zbrar[m + 1].key)[key, adr][key0])

Rule argument

Additional information

Used simplifier rules: fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)