Nuprl Lemma : geo-sep-irreflexive
∀e:GeometryPrimitives. (BasicGeometryAxioms(e) ⇒ (∀a:Point. (¬a # 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],
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
basic-geo-axioms: BasicGeometryAxioms(g),
and: P ∧ Q,
cand: A c∧ B,
geo-sep: a # b,
not: ¬A,
false: False,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
geo-ge: ab ≥ cd
Latex:
\mforall{}e:GeometryPrimitives. (BasicGeometryAxioms(e) {}\mRightarrow{} (\mforall{}a:Point. (\mneg{}a \# a)))
Date html generated:
2020_05_20-AM-09_41_38
Last ObjectModification:
2020_02_05-AM-11_29_55
Theory : euclidean!plane!geometry
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