Nuprl Lemma : geo-axiom-contrapositive
∀g:GeometryPrimitives. (BasicGeometryAxioms(g) ⇒ (∀a,b,c:Point. ((¬b # c) ⇒ (¬ba>ac))))
Proof
Definitions occuring in Statement :
basic-geo-axioms: BasicGeometryAxioms(g),
geo-sep: a # b,
geo-gt-prim: ab>cd,
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,
not: ¬A,
false: False,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
basic-geo-axioms: BasicGeometryAxioms(g),
and: P ∧ Q
Latex:
\mforall{}g:GeometryPrimitives. (BasicGeometryAxioms(g) {}\mRightarrow{} (\mforall{}a,b,c:Point. ((\mneg{}b \# c) {}\mRightarrow{} (\mneg{}ba>ac))))
Date html generated:
2020_05_20-AM-09_41_42
Last ObjectModification:
2020_01_24-PM-09_10_27
Theory : euclidean!plane!geometry
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