Nuprl Lemma : geo-sep_functionality
∀e:EuclideanPlane. ∀a1,a2,b1,b2:Point. (a1 ≡ a2 ⇒ b1 ≡ b2 ⇒ (a1 # b1 ⇐⇒ a2 # b2))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-eq: a ≡ b,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
rev_implies: P ⇐ Q
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a1,a2,b1,b2:Point. (a1 \mequiv{} a2 {}\mRightarrow{} b1 \mequiv{} b2 {}\mRightarrow{} (a1 \# b1 \mLeftarrow{}{}\mRightarrow{} a2 \# b2))
Date html generated:
2020_05_20-AM-09_48_20
Last ObjectModification:
2020_01_13-PM-03_12_48
Theory : euclidean!plane!geometry
Home
Index