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Theorem range-cong-dups

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

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 9
Used lemmas: congmod-def-mod, mod-le-same, mod-pos,
Used spec theorems:
- intlist/range-dups
- intlist/map-in
- list-del/intlista/dups-def
Used simplifier rules:
- int-abs/forward-le-01
- int-abs/forward-lels
- int-basic1/ls-01
- int-abs/lels-01
- int-abs/lels
- nat-basic1/zero
- nat-basic1/one
- intnat/num-n2i-ls-02
- int-abs/forward-le-05
- oelem/intlista/transitivity
- int-basic1/forward-pos
- list-data/intlista/l
- nat-basic1/f
- intlist/map-at
- intlist/map-length
- list-del/intlista/get-nodups