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Proof step 1 from proof range-cong-dups (conclusion)

0 < j, j < n→i(# ints), ¬ dups(ints) ⊦ ∃ i1, i2. i1 ≠ i2 ∧ ≡mod(i1, i2, j)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 2:
∀ i. i ∈ ints → 0 ≤ i ∧ i < j, 0 ≤ j, j < n→i(# ints) ⊦ dups(ints)
Proof step 3:
0 < j, j < n→i(# ints), ¬ dups(ints) ⊦ (∀ i. i ∈ mapFun(λ i. i |%| j, ints) → 0 ≤ i ∧ i < j) ∧ 0 ≤ j ∧ j < n→i(# mapFun(λ i. i |%| j, ints)), ∃ i1, i2. i1 ≠ i2 ∧ ≡mod(i1, i2, j)
Proof step 6:
dups(mapFun(λ i. i |%| j, ints)), 0 < j, j < n→i(# ints), ¬ dups(ints) ⊦ ∃ i1, i2. i1 ≠ i2 ∧ ≡mod(i1, i2, j)

Rule argument

spec: intlist inst: name: range-dups seq: ∀ i. i ∈ ints → 0 ≤ i ∧ i < j, 0 ≤ j, j < n→i(# ints) ⊦ dups(ints) subst: [ints, j] → [mapFun(λ i. i |%| j, ints), j] flags:

Additional information

Used terms: mapFun(λ i. i |%| j, ints), j