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Proof step 7 from proof range-cong-dups (previous step)

0 < j, j < n→i(# ints), dups(mapFun(λ i. i |%| j, ints)) ⊦ # ints = 1, ints = [], dups(ints), ∃ i1, i2. i1 ≠ i2 ∧ ≡mod(i1, i2, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ dups(ints) ↔ (∃ m, n. m < # ints ∧ n < # ints ∧ m ≠ n ∧ ints[m] = ints[n])
Proof step 9:
0 < j, j < n→i(# ints), ∃ m, n. m < # mapFun(λ i. i |%| j, ints) ∧ n < # mapFun(λ i. i |%| j, ints) ∧ m ≠ n ∧ mapFun(λ i. i |%| j, ints)[m] = mapFun(λ i. i |%| j, ints)[n] ⊦ # ints = 1, ints = [], dups(ints), ∃ i1, i2. i1 ≠ i2 ∧ ≡mod(i1, i2, j)

Rule argument

spec: list-del inst: intlista name: dups-def seq: ⊦ dups(ints) ↔ (∃ m, n. m < # ints ∧ n < # ints ∧ m ≠ n ∧ ints[m] = ints[n]) subst: [ints] → [mapFun(λ i. i |%| j, ints)] flags: rewrite

Additional information

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