Nuprl Lemma : geo-length_functionality
∀e:BasicGeometry. ∀[a,b,c,d:Point]. (|ab| = |cd| ∈ Length) supposing (b ≡ d and a ≡ c)
Proof
Definitions occuring in Statement :
geo-length: |s|,
geo-length-type: Length,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-eq: a ≡ b,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
basic-geometry: BasicGeometry,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
guard: {T}
Latex:
\mforall{}e:BasicGeometry. \mforall{}[a,b,c,d:Point]. (|ab| = |cd|) supposing (b \mequiv{} d and a \mequiv{} c)
Date html generated:
2020_05_20-AM-09_52_02
Last ObjectModification:
2020_01_13-PM-03_24_49
Theory : euclidean!plane!geometry
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