Nuprl Lemma : geo-plsep_functionality
∀e:EuclideanPlane. ∀a1,a2:Point. ∀l1,l2:Line. (a1 ≡ a2 ⇒ l1 ≡ l2 ⇒ (a1 # l1 ⇐⇒ a2 # l2))
Proof
Definitions occuring in Statement :
geo-plsep: p # l,
geo-line-eq: l ≡ m,
geo-line: Line,
euclidean-plane: EuclideanPlane,
geo-eq: 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,
geo-plsep: p # l,
member: t ∈ T,
guard: {T},
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
prop: ℙ,
rev_implies: P ⇐ Q,
oriented-plane: OrientedPlane,
geo-line: Line,
pi1: fst(t),
pi2: snd(t)
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a1,a2:Point. \mforall{}l1,l2:Line. (a1 \mequiv{} a2 {}\mRightarrow{} l1 \mequiv{} l2 {}\mRightarrow{} (a1 \# l1 \mLeftarrow{}{}\mRightarrow{} a2 \# l2))
Date html generated:
2020_05_20-AM-10_46_11
Last ObjectModification:
2020_01_13-PM-05_49_46
Theory : euclidean!plane!geometry
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