Nuprl Lemma : geo-out-trivial
∀e:BasicGeometry. ∀a,b:Point. (a ≠ b ⇒ out(a bb))
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
basic-geometry: BasicGeometry,
geo-sep: a ≠ b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
geo-out: out(p ab),
and: P ∧ Q,
cand: A c∧ B,
not: ¬A,
member: t ∈ T,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
geo-between-trivial,
not_wf,
geo-between_wf,
geo-sep_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
basic-geometry-subtype,
subtype_rel_transitivity,
basic-geometry_wf,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-point_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
hypothesis,
cut,
sqequalHypSubstitution,
productElimination,
thin,
independent_functionElimination,
introduction,
extract_by_obid,
dependent_functionElimination,
hypothesisEquality,
isectElimination,
productEquality,
applyEquality,
because_Cache,
sqequalRule,
instantiate,
independent_isectElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b:Point. (a \mneq{} b {}\mRightarrow{} out(a bb))
Date html generated:
2018_05_22-AM-11_58_21
Last ObjectModification:
2018_04_19-PM-02_08_15
Theory : euclidean!plane!geometry
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