Nuprl Lemma : geo-out_transitivity
∀e:BasicGeometry. ∀a,b,c,d:Point. (out(a bc) ⇒ out(a cd) ⇒ out(a bd))
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
basic-geometry: BasicGeometry,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
geo-out: out(p ab),
and: P ∧ Q,
not: ¬A,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
guard: {T},
uimplies: b supposing a,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
basic-geometry-: BasicGeometry-,
cand: A c∧ B
Lemmas referenced :
geo-between_wf,
istype-void,
geo-out_wf,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
basic-geometry-subtype,
subtype_rel_transitivity,
basic-geometry_wf,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-between-symmetry,
geo-between-inner-trans,
geo-between-exchange3,
subtype_rel_self,
basic-geometry-_wf,
geo-between-exchange4,
geo-between-same-side,
geo-between-middle
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
hypothesis,
independent_functionElimination,
universeIsType,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
sqequalRule,
voidElimination,
productIsType,
functionIsType,
inhabitedIsType,
instantiate,
independent_isectElimination,
dependent_functionElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,d:Point. (out(a bc) {}\mRightarrow{} out(a cd) {}\mRightarrow{} out(a bd))
Date html generated:
2019_10_16-PM-01_23_08
Last ObjectModification:
2019_08_27-AM-09_57_48
Theory : euclidean!plane!geometry
Home
Index