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Proof step 14 from proof range-put (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
zbrar[m].key < key, m + 1 < # zbrar ⊦ zbrar[m + 1].key < key, (key0 = key ∨ key0 ∈ ri ∧ zbrar[m].key < key0 → key0 ∈ (ri |> zbrar[m].key)[key, adr]) ∧ (key0 ∈ (ri |> zbrar[m].key)[key, adr] → ri[key, adr][key0] = (ri |> zbrar[m].key)[key, adr][key0])

Rule argument

Additional information

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