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Proof step 34 from proof prepost-resize (previous step)

kar[m0] = key-index(key0, m2), kar[m1] = key-index(key, m2), 2exp-size(n0), 2exp-size(# kar), m0 < n0, m1 < n0, m0 + 1 < n0, m1 + 1 < n0, m0 + 1 < minsize, m1 < minsize, m1 < # kar, m1 + 1 < minsize, m0 < m, m < minsize, m < n0, m1 < m, m0 < minsize, m0 < # kar, heap-order(kar, m), valid-idx(kar, ar, m), minsize ≤ n0, m ≤ # kar, ∀ m0, m1. m0 < # kar ∧ m0 < m ∧ m1 < # kar ∧ m1 < m ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx ⊦ m1 = m0

User applied rule all left

And closed the goal!

Rule argument

pos: left 23 terms: m1, m0 abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ key-index(key, m).idx = m; (s) Used terms: m1, m0