Nuprl Lemma : geo-ab-eq-x
∀e:BasicGeometry. ∀a,b:Point. (a ≡ b ⇒ (X = |ab| ∈ Length))
Proof
Definitions occuring in Statement :
geo-length: |s|,
geo-length-type: Length,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-X: X,
geo-eq: a ≡ b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
basic-geometry: BasicGeometry,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q)
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b:Point. (a \mequiv{} b {}\mRightarrow{} (X = |ab|))
Date html generated:
2020_05_20-AM-09_58_04
Last ObjectModification:
2020_01_13-PM-03_33_05
Theory : euclidean!plane!geometry
Home
Index