Nuprl Lemma : stable__geo-perp-in
∀e:BasicGeometry. ∀x:Point. ∀[a,b,c,d:Point]. Stable{ab ⊥x cd}
Proof
Definitions occuring in Statement :
geo-perp-in: ab ⊥x cd,
basic-geometry: BasicGeometry,
geo-point: Point,
stable: Stable{P},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
geo-perp-in: ab ⊥x cd,
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
uimplies: b supposing a
Lemmas referenced :
stable__and,
geo-colinear_wf,
all_wf,
geo-point_wf,
right-angle_wf,
stable__colinear,
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,
stable__all,
stable__right-angle
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
productEquality,
lambdaEquality,
independent_functionElimination,
dependent_functionElimination,
instantiate,
independent_isectElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}x:Point. \mforall{}[a,b,c,d:Point]. Stable\{ab \mbot{}x cd\}
Date html generated:
2018_05_22-PM-00_03_31
Last ObjectModification:
2018_05_17-AM-09_20_49
Theory : euclidean!plane!geometry
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