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Theorem ordered-ex-divide-lels
ordered≤(x) ⊦ ∃ y, z. x = y + z ∧ (∀ b. b ∈ y → b < a ∨ b = a) ∧ (∀ b. b ∈ z → a < 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: 8
Proof steps: 19
Used lemmas:
orderedle-ls
,
cons-02
,
app-01
,
le-e
,
Used spec theorems:
Used simplifier rules:
list
/
c
oelem
/
sls
oelem
/
nll
list
/
in-append
list
/
in-rec
list
/
in-empty
list
/
app-08
list
/
Nil
list
/
in-11
list
/
a
oelem
/
transitivity
oelem
/
irreflexivity