Nuprl Lemma : geo-between-implies-sep
∀e:BasicGeometry. ∀a,b,c:Point. (a ≠ b ⇒ a_b_c ⇒ a ≠ c)
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-between: a_b_c,
geo-sep: a ≠ b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
implies: P ⇒ Q
Lemmas referenced :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
geo-between-sep,
geo-sep_wf,
geo-between_wf
Rules used in proof :
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
isectElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut,
because_Cache,
independent_functionElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c:Point. (a \mneq{} b {}\mRightarrow{} a\_b\_c {}\mRightarrow{} a \mneq{} c)
Date html generated:
2017_10_02-PM-04_43_20
Last ObjectModification:
2017_08_05-AM-08_42_50
Theory : euclidean!plane!geometry
Home
Index