Nuprl Lemma : geo-left-out-1
∀e:EuclideanPlane. ∀a,b,b',p:Point. (p leftof ba ⇒ out(a bb') ⇒ p leftof b'a)
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],
member: t ∈ T,
implies: P ⇒ Q,
geo-out: out(p ab),
and: P ∧ Q,
not: ¬A,
geo-sep: a ≠ b,
cand: A c∧ B,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
basic-geometry: BasicGeometry,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
geo-left-out-better-1,
geo-sep-sym,
not_wf,
geo-between_wf,
geo-out_wf,
geo-left_wf,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
productElimination,
sqequalRule,
independent_pairFormation,
productEquality,
isectElimination,
applyEquality,
because_Cache,
instantiate,
independent_isectElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,b',p:Point. (p leftof ba {}\mRightarrow{} out(a bb') {}\mRightarrow{} p leftof b'a)
Date html generated:
2018_05_22-AM-11_59_20
Last ObjectModification:
2018_04_20-PM-02_01_38
Theory : euclidean!plane!geometry
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