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Proof step 2 from proof no-dups-keyset-size (previous step)

m ≤ # kar ⊦ no-dups(kar, m) ↔ # keyset(kar, m) = m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
m ≤ # kar ⊦ (∀ m0, m1. m0 < # kar ∧ m0 < m ∧ m1 < # kar ∧ m1 < m ∧ m0 ≠ m1 → kar[m0] ≠ kar[m1]) ↔ # keyset(kar, m) = m

Rule argument

Additional information

Used simplifier rules: no-dups: ⊦ no-dups(kar, n) ↔ (∀ m0, m1. m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0] ≠ kar[m1]);