Nuprl Lemma : left-opposite-between
∀e:OrientedPlane. ∀a,b,p,q,x:Point. (a_q_x ⇒ a leftof bp ⇒ q leftof pb ⇒ x leftof pb)
Proof
Definitions occuring in Statement :
oriented-plane: OrientedPlane,
geo-left: a leftof bc,
geo-between: a_b_c,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
oriented-plane: Error :oriented-plane,
prop: ℙ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
geo-point_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry-_wf,
Error :oriented-plane_wf,
subtype_rel_transitivity,
basic-geometry--subtype,
geo-between_wf,
geo-left_wf,
geo-between-exchange3,
geo-between-inner-trans,
Error :oriented-plane-subtype,
geo-between-symmetry,
Error :use-plane-sep,
left-convex3
Rules used in proof :
instantiate,
setElimination,
independent_isectElimination,
because_Cache,
isectElimination,
sqequalRule,
applyEquality,
rename,
productElimination,
hypothesis,
independent_functionElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:OrientedPlane. \mforall{}a,b,p,q,x:Point. (a\_q\_x {}\mRightarrow{} a leftof bp {}\mRightarrow{} q leftof pb {}\mRightarrow{} x leftof pb)
Date html generated:
2017_10_02-PM-04_48_05
Last ObjectModification:
2017_08_05-AM-10_20_37
Theory : euclidean!plane!geometry
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