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Proof step 24 from proof key-set-write-nodups (previous step)

kar[m1] = key-index(key0, m3), kar[m] = key-index(key, m3), m < m0, m1 < # kar, m1 < m0, n + 1 < # kar, n < # kar, m0 < # kar, n < m0, m + 1 < # kar, m < # kar, m1 + 1 < # kar, ∀ m, m1. m < # kar ∧ ¬ m0 < m ∧ m1 < # kar ∧ ¬ m0 < m1 ∧ m ≠ m1 → kar[m].idx ≠ kar[m1].idx ⊦ keyset(kar[n, ki], m0) ++ kar[m0] = ((keyset(kar, m0) ++ kar[m0]) -- kar[n]) ++ ki, m = m1, m0 = n

User applied rule all left

And closed the goal!

Rule argument

pos: left 13 terms: m, m1 abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m; (s)% ⊦ key-index(key, m).idx = m; (s) Used terms: m, m1