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Proof step 13 from proof range-put (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
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])

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m