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Proof step 17 from proof prepost-update (previous step)

ar[m] = elemindex(a, m1), kar[m1] = key-index(key0, m), key-index(key0, m) = kar[m2], 2exp-size(# kar), m2 < m0, m2 < # kar, m2 < m1, heap-order(kar, m0), no-dups-idx(kar, m0), m0 ≤ # kar, m0 ≤ m1, ∀ m. m < m0 → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ # keyset(kar, m0) = 0, keyset(kar, m0) = ∅

User applied rule all left

And closed the goal!

Rule argument

pos: left 12 terms: m2 abort: F discard: T computed: T

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ key-index(key, m).idx = m; (s)% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ elemindex(a, m).idx = m; (s)% ⊦ ¬ n < n; (s) Used terms: m2