Nuprl Lemma : basic-geo-sep-sym
∀e:GeometryPrimitives. (BasicGeometryAxioms(e) ⇒ (∀a,b:Point. (a # b ⇒ b # a)))
Proof
Definitions occuring in Statement :
basic-geo-axioms: BasicGeometryAxioms(g),
geo-sep: a # b,
geo-primitives: GeometryPrimitives,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
geo-ge: ab ≥ cd,
not: ¬A,
false: False,
uall: ∀[x:A]. B[x],
prop: ℙ,
geo-sep: a # b,
geo-congruent: ab ≅ cd,
basic-geo-axioms: BasicGeometryAxioms(g),
and: P ∧ Q,
cand: A c∧ B,
geo-length-sep: ab # cd),
or: P ∨ Q,
guard: {T}
Latex:
\mforall{}e:GeometryPrimitives. (BasicGeometryAxioms(e) {}\mRightarrow{} (\mforall{}a,b:Point. (a \# b {}\mRightarrow{} b \# a)))
Date html generated:
2020_05_20-AM-09_41_56
Last ObjectModification:
2020_01_27-PM-10_41_43
Theory : euclidean!plane!geometry
Home
Index