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Proof step 10 from proof no-dups-keyset-size (previous step)

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

User applied rule all left

And closed the goal!

Rule argument

pos: left 9 terms: m1, m abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m; (s) Used terms: m1, m