Nuprl Lemma : geo-left-convex
∀g:OrientedPlane. ∀a,b:Point. IsConvex(x.x leftof ab)
Proof
Definitions occuring in Statement :
geo-convex: IsConvex(x.P[x]),
oriented-plane: OrientedPlane,
geo-left: a leftof bc,
geo-point: Point,
all: ∀x:A. B[x]
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
oriented-plane: Error :oriented-plane,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
geo-convex: IsConvex(x.P[x]),
all: ∀x:A. B[x]
Lemmas referenced :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
Error :o-geo-structure_wf,
Error :oriented-plane_wf,
subtype_rel_transitivity,
Error :oriented-plane-subtype1,
Error :o-geo-structure-subtype,
geo-point_wf,
geo-between_wf,
geo-left_wf,
left-between-weak
Rules used in proof :
independent_isectElimination,
instantiate,
sqequalRule,
because_Cache,
applyEquality,
rename,
setElimination,
isectElimination,
hypothesis,
independent_functionElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:OrientedPlane. \mforall{}a,b:Point. IsConvex(x.x leftof ab)
Date html generated:
2017_10_02-PM-06_49_15
Last ObjectModification:
2017_08_06-PM-07_29_02
Theory : euclidean!plane!geometry
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