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Proof step 26 from proof nodups-interval-size (previous step)

n→i(# ints - 1) + j0 < j1, max(ints) < n→i(# ints) + j0, j0 < j1, max(ints) ≤ j1, j0 < max(ints), j1 < n→i(# ints) + j0, ∀ i. i ∈ ints → j0 < i ∧ i ≤ j1, ∀ ints0, j0, j1. # ints0 < # ints → ¬ dups(ints0) ∧ (∀ i. i ∈ ints0 → j0 < i ∧ i ≤ j1) ∧ ints0 ≠ [] → n→i(# ints0) ≤ j1 - j0 ⊦ ints = [], dups(ints)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: intnat inst: name: n2i-sub seq: ⊦ n ≤ m → n→i(m - n) = n→i(m) - n→i(n) subst: [n, m] → [1, # ints] flags: rewrite

Additional information

Used simplifier rules: sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%succ-02: ⊦ i < j + 1 ↔ i ≤ j; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1%l: ⊦ # ints = 0 ↔ ints = []; from specification list-data[intlista] Used terms: 1, # ints