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Proof step 16 from proof keep-range (previous step)

zbr.key = zbrar[m].key, m < # zbrar, n < # zbrar ⊦ key-range(zbrar[m, zbr], n, n + 1, ri) = key-range(zbrar, n, n + 1, ri)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ n ≠ 0 ∧ n < # zbrar → key-range(zbrar, n, n + 1, ri) = ri |> zbrar[n - 1].key
Proof step 18:
zbr.key = zbrar[m].key, n < # zbrar, m < # zbrar, n < # zbrar[m, zbr] ⊦ n = 0, ri |> zbrar[m, zbr][n - 1].key = key-range(zbrar, n, n + 1, ri)

Rule argument

spec: <toplevel> name: range-last seq: ⊦ n ≠ 0 ∧ n < # zbrar → key-range(zbrar, n, n + 1, ri) = ri |> zbrar[n - 1].key subst: [ri, n, zbrar] → [ri, n, zbrar[m, zbr]] flags: <all paths>

Additional information

Used simplifier rules: range-one: ⊦ key-range(zbrar, 0, 1, ri) = ri;% ⊦ # zbrar[n, zbr] = # zbrar; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: ri, n, zbrar[m, zbr]