Nuprl Lemma : eu-out-refl
∀e:EuclideanPlane. ∀a,b,c:Point. (out(a bc) ⇒ out(a cb))
Proof
Definitions occuring in Statement :
eu-out: out(p ab),
euclidean-plane: EuclideanPlane,
eu-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
eu-out: out(p ab),
and: P ∧ Q,
cand: A c∧ B,
not: ¬A,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
euclidean-plane: EuclideanPlane
Lemmas referenced :
and_wf,
not_wf,
eu-between-eq_wf,
eu-out_wf,
eu-point_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
hypothesis,
independent_pairFormation,
independent_functionElimination,
lemma_by_obid,
isectElimination,
setElimination,
rename,
hypothesisEquality,
because_Cache
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c:Point. (out(a bc) {}\mRightarrow{} out(a cb))
Date html generated:
2016_05_18-AM-06_42_03
Last ObjectModification:
2015_12_28-AM-09_23_32
Theory : euclidean!geometry
Home
Index