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Proof step 8 from proof keys-drop-upper (previous step)

m + nused0 < # zbrar, m + nused0 < n, m < # zbrar, n ≤ # zbrar, ∀ m, n, zbrar, zbr. m + nused0 ≤ n ∧ n ≤ # zbrar ∧ m + nused0 ≤ # zbrar → keys(zbrar[n, zbr], m, nused0) = keys(zbrar, m, nused0) ⊦ keys(zbrar[n, zbr], m + 1, nused0) ++ zbrar[m].key = keys(zbrar, m + 1, nused0) ++ zbrar[m].key

User applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: m + 1, n, zbrar, zbr abort: F discard: F computed: F

Additional information

Used simplifier rules: ⊦ m + 1 ≤ n ↔ m < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m + 1, n, zbrar, zbr