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Proof step 71 from proof prepost-resize (previous step)

kar[m1 / 2] = key-index(key0, m2), kar[1 + m1] = key-index(key, m0), 2exp-size(# kar), 2exp-size(n0), m1 + 1 < # kar, m1 + 1 < minsize, m < n0, m < minsize, m1 + 1 < m, key < key0, 2 + m1 < n0, 2 + m1 < minsize, m1 + 1 < n0, m1 / 2 < n0, m1 < m * 2, no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, minsize ≤ n0, ∀ m0. m0 < m ∧ m0 ≠ 0 → ¬ kar[m0].key < kar[(m0 - 1) / 2].key ⊦

User applied rule all left

And closed the goal!

Rule argument

pos: left 20 terms: m1 + 1 abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ m + 1 ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ n + 0 = n; (s)% ⊦ key-index(key, m).key = key; (s) Used terms: m1 + 1