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Proof step 16 from proof key-set-write-nodups (previous step)

kar[n] = kar[m], m < # kar, n < # kar, m < n, m + 1 < # kar, ∀ n0, kar, ki. n0 < n ∧ n0 < # kar ∧ n ≤ # kar ∧ (∀ m2, m1. m2 < # kar ∧ m2 < n ∧ m1 < # kar ∧ m1 < n ∧ m2 ≠ m1 → kar[m2].idx ≠ kar[m1].idx) → keyset(kar[n0, ki], n) = (keyset(kar, n) -- kar[n0]) ++ ki, ∀ m, m1. m < # kar ∧ ¬ n < m ∧ m1 < # kar ∧ ¬ n < m1 ∧ m ≠ m1 → kar[m].idx ≠ kar[m1].idx ⊦ # keyset(kar, n) = 0, keyset(kar, n) ++ ki = (keyset(kar, n) -- kar[m]) ++ ki, keyset(kar, n) = ∅

User applied rule all left

And closed the goal!

Rule argument

pos: left 7 terms: n, 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: n, m