Nuprl Lemma : geo-between-sep
∀g:EuclideanPlane. ∀a,b,x:Point. (a_x_b ⇒ a ≠ x ⇒ a ≠ b)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
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],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
geo-ge-sep,
geo-between-implies-ge,
geo-point_wf,
geo-between_wf,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-sep_wf
Rules used in proof :
independent_functionElimination,
dependent_functionElimination,
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,x:Point. (a\_x\_b {}\mRightarrow{} a \mneq{} x {}\mRightarrow{} a \mneq{} b)
Date html generated:
2017_10_02-PM-03_28_58
Last ObjectModification:
2017_08_04-PM-09_35_13
Theory : euclidean!plane!geometry
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