Nuprl Lemma : geo-left-out-4
∀e:EuclideanPlane. ∀a,b,p,a',b':Point. (p leftof ab ⇒ out(p aa') ⇒ out(p bb') ⇒ p leftof a'b')
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
euclidean-plane: EuclideanPlane,
geo-left: a leftof bc,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
guard: {T},
and: P ∧ Q,
uall: ∀[x:A]. B[x],
basic-geometry: BasicGeometry,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
left-all-symmetry,
geo-left-out-2,
geo-left-out,
euclidean-plane-axioms,
geo-out_wf,
geo-left_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_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,
productElimination,
universeIsType,
isectElimination,
sqequalRule,
applyEquality,
instantiate,
independent_isectElimination,
inhabitedIsType,
because_Cache
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,p,a',b':Point. (p leftof ab {}\mRightarrow{} out(p aa') {}\mRightarrow{} out(p bb') {}\mRightarrow{} p leftof a'b')
Date html generated:
2019_10_16-PM-01_25_24
Last ObjectModification:
2018_10_25-AM-09_54_45
Theory : euclidean!plane!geometry
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