Nuprl Lemma : lsep-colinear-sep1
∀g:OrientedPlane. ∀a,b,c:Point. ∀y:{y:Point| Colinear(y;b;c)} . (a # bc ⇒ a ≠ y)
Proof
Definitions occuring in Statement :
oriented-plane: OrientedPlane,
geo-lsep: a # bc,
geo-colinear: Colinear(a;b;c),
geo-sep: a ≠ b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
sq_stable: SqStable(P),
squash: ↓T,
prop: ℙ
Lemmas referenced :
lsep-colinear-sep,
sq_stable__colinear,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
oriented-plane-subtype,
subtype_rel_transitivity,
oriented-plane_wf,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-lsep_wf,
geo-colinear_wf,
geo-point_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
setElimination,
rename,
applyEquality,
instantiate,
isectElimination,
independent_isectElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
universeIsType,
setIsType,
inhabitedIsType,
because_Cache
Latex:
\mforall{}g:OrientedPlane. \mforall{}a,b,c:Point. \mforall{}y:\{y:Point| Colinear(y;b;c)\} . (a \# bc {}\mRightarrow{} a \mneq{} y)
Date html generated:
2019_10_16-PM-01_15_15
Last ObjectModification:
2018_10_25-AM-11_20_29
Theory : euclidean!plane!geometry
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