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Proof step 3 from proof keys-drop-lower (previous step)

m + n + nused ≤ # zbrar ⊦ keys(zbrar[m, zbr], m + n, nused) = keys(zbrar, m + n, nused), n = 0

User applied rule structural induction

And obtained the following new goals

Proof step 4:
m + n + nused0 +1 ≤ # zbrar, ∀ m, n, zbrar, zbr. m + n + nused0 ≤ # zbrar → keys(zbrar[m, zbr], m + n, nused0) = keys(zbrar, m + n, nused0) ∨ n = 0 ⊦ keys(zbrar[m, zbr], m + n, nused0 +1) = keys(zbrar, m + n, nused0 +1), n = 0

Rule argument

indvar: nused

Additional information

Used simplifier rules: keys-base: ⊦ keys(zbrar, m, 0) = ∅;%nat freely generated by 0, +1;;