Nuprl Lemma : geo-congruent-trivial
∀e:EuclideanPlane. ∀[a,b:Point]. aa ≅ bb
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-point: Point,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
euclidean-plane: EuclideanPlane,
stable: Stable{P},
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
geo-congruent: ab ≅ cd,
guard: {T},
or: P ∨ Q,
geo-eq: a ≡ b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
exists: ∃x:A. B[x]
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b:Point]. aa \mcong{} bb
Date html generated:
2020_05_20-AM-09_51_20
Last ObjectModification:
2020_01_13-PM-03_25_07
Theory : euclidean!plane!geometry
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