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

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

User applied rule structural induction

And obtained the following new goals

Proof step 4:
m + nused0 +1 ≤ # zbrar, n ≤ # zbrar, m + nused0 +1 ≤ n, ∀ 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, nused0 +1) = keys(zbrar, m, nused0 +1)

Rule argument

indvar: nused

Additional information

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