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Theorem notdups-map-injective
⊦ ¬ dups(x) → (¬ dups(x.map(f)) ↔ (∀ a, b. a ∈ x ∧ b ∈ x ∧ a ≠ b → f(a) ≠ f(b)))
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: 15
Proof steps: 35
Used lemmas:
dups
,
Used spec theorems:
list
/
in-def
Used simplifier rules:
list
/
a
list
/
c
list
/
map-rec
list
/
map-append
list
/
in-01
list
/
in-append
list
/
map-base
list
/
app-02
list
/
e
list
/
in-rec
list
/
in-14
list
/
in-empty
list
/
c-06
list
/
Nil
list
/
neq
list
/
map-in
list
/
len-01