Nuprl Lemma : geo-strict-between-sep2
∀e:GeometryPrimitives. ∀a,b,c:Point. (a-b-c ⇒ a ≠ b)
Proof
Definitions occuring in Statement :
geo-strict-between: a-b-c,
geo-sep: a ≠ b,
geo-primitives: GeometryPrimitives,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
and: P ∧ Q,
geo-strict-between: a-b-c,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
geo-primitives_wf,
geo-point_wf,
geo-strict-between_wf
Rules used in proof :
productElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:GeometryPrimitives. \mforall{}a,b,c:Point. (a-b-c {}\mRightarrow{} a \mneq{} b)
Date html generated:
2017_10_02-PM-04_42_28
Last ObjectModification:
2017_08_08-PM-00_35_28
Theory : euclidean!plane!geometry
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