Nuprl Lemma : sq_stable__geo-perp-in
∀e:BasicGeometry. ∀x:Point. ∀[a,b,c,d:Point]. SqStable(ab ⊥x cd)
Proof
Definitions occuring in Statement :
geo-perp-in: ab ⊥x cd,
basic-geometry: BasicGeometry,
geo-point: Point,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
implies: P ⇒ Q
Lemmas referenced :
stable__geo-perp-in,
geo-point_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,
sq_stable__from_stable,
geo-perp-in_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isect_memberFormation,
isectElimination,
applyEquality,
because_Cache,
sqequalRule,
instantiate,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}x:Point. \mforall{}[a,b,c,d:Point]. SqStable(ab \mbot{}x cd)
Date html generated:
2018_05_22-PM-00_03_39
Last ObjectModification:
2018_05_19-PM-08_48_17
Theory : euclidean!plane!geometry
Home
Index