Nuprl Lemma : geo-congruent-flip
∀e:GeometryPrimitives. (BasicGeometryAxioms(e) ⇒ (∀[a,b:Point]. ab ≅ ba))
Proof
Definitions occuring in Statement :
basic-geo-axioms: BasicGeometryAxioms(g),
geo-congruent: ab ≅ cd,
geo-primitives: GeometryPrimitives,
geo-point: Point,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
basic-geo-axioms: BasicGeometryAxioms(g),
and: P ∧ Q,
cand: A c∧ B,
geo-congruent: ab ≅ cd,
not: ¬A,
geo-length-sep: ab # cd),
or: P ∨ Q,
prop: ℙ,
false: False
Latex:
\mforall{}e:GeometryPrimitives. (BasicGeometryAxioms(e) {}\mRightarrow{} (\mforall{}[a,b:Point]. ab \mcong{} ba))
Date html generated:
2020_05_20-AM-09_41_50
Last ObjectModification:
2020_01_27-AM-10_59_45
Theory : euclidean!plane!geometry
Home
Index