Nuprl Lemma : geo-perp-in_wf
∀[e:BasicGeometry]. ∀[x,a,b,c,d:Point]. (ab ⊥x cd ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-perp-in: ab ⊥x cd,
basic-geometry: BasicGeometry,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
geo-perp-in: ab ⊥x cd,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x],
guard: {T},
uimplies: b supposing a
Lemmas referenced :
geo-colinear_wf,
all_wf,
geo-point_wf,
right-angle_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
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
lambdaEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
independent_isectElimination,
isect_memberEquality
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[x,a,b,c,d:Point]. (ab \mbot{}x cd \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-00_03_24
Last ObjectModification:
2018_05_14-PM-03_18_15
Theory : euclidean!plane!geometry
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