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Proof step 17 from proof no-dups-keyset-size (previous step)

# keyset(kar, m0) = m0, kar[m0] = kar[m], m < # kar, m0 < # kar, m < m0, m + 1 < # kar, ∀ m2, m1. m2 < # kar ∧ m2 < m0 ∧ m1 < # kar ∧ m1 < m0 ∧ m2 ≠ m1 → kar[m2] ≠ kar[m1], ∀ m, m1. m < # kar ∧ ¬ m0 < m ∧ m1 < # kar ∧ ¬ m0 < m1 ∧ m ≠ m1 → kar[m] ≠ kar[m1] ⊦ keyset(kar, m0) = ∅

User applied rule all left

And closed the goal!

Rule argument

pos: left 8 terms: m0, m abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s)% ⊦ m < n → ¬ n < m; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic Used terms: m0, m