Nuprl Lemma : sq_stable__incident
∀e:EuclideanPlane. ∀a:Point. ∀l:LINE. SqStable(a I l)
Proof
Definitions occuring in Statement :
geo-incident: p I L,
geoline: LINE,
euclidean-plane: EuclideanPlane,
geo-point: Point,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-point_wf,
geoline_wf,
stable__incident,
geo-incident_wf,
sq_stable__from_stable
Rules used in proof :
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
dependent_functionElimination,
independent_functionElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a:Point. \mforall{}l:LINE. SqStable(a I l)
Date html generated:
2018_07_29-AM-09_36_06
Last ObjectModification:
2018_06_21-AM-09_05_09
Theory : euclidean!plane!geometry
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