Nuprl Lemma : lsep-symmetry2
∀g:EuclideanPlane. ∀a,b,c:Point. (a # bc ⇒ a # cb)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-lsep: a # bc,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
guard: {T},
or: P ∨ Q,
geo-lsep: a # bc,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
geo-point_wf,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-lsep_wf,
geo-left_wf
Rules used in proof :
independent_isectElimination,
instantiate,
inlFormation,
because_Cache,
applyEquality,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
inrFormation,
hypothesis,
cut,
sqequalRule,
thin,
unionElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c:Point. (a \# bc {}\mRightarrow{} a \# cb)
Date html generated:
2017_10_02-PM-03_29_35
Last ObjectModification:
2017_08_07-AM-10_51_42
Theory : euclidean!plane!geometry
Home
Index