Nuprl Lemma : geo-out-if-between
∀e:BasicGeometry. ∀p,a,b,c:Point. (a-p-c ⇒ b-p-c ⇒ out(p ab))
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
basic-geometry: BasicGeometry,
geo-strict-between: a-b-c,
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,
cand: A c∧ B,
member: t ∈ T,
basic-geometry: BasicGeometry,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
euclidean-plane: EuclideanPlane,
basic-geometry-: BasicGeometry-,
prop: ℙ
Lemmas referenced :
geo-sep-sym,
geo-strict-between-sep2,
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-same-side2,
geo-strict-between-implies-between,
subtype_rel_self,
geo-between-symmetry,
geo-strict-between-sep3,
geo-strict-between_wf,
geo-point_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
because_Cache,
independent_functionElimination,
applyEquality,
hypothesis,
instantiate,
isectElimination,
independent_isectElimination,
sqequalRule,
independent_pairFormation,
universeIsType,
inhabitedIsType
Latex:
\mforall{}e:BasicGeometry. \mforall{}p,a,b,c:Point. (a-p-c {}\mRightarrow{} b-p-c {}\mRightarrow{} out(p ab))
Date html generated:
2019_10_16-PM-01_23_34
Last ObjectModification:
2019_07_26-PM-01_55_19
Theory : euclidean!plane!geometry
Home
Index