Nuprl Lemma : geo-opp-side_wf
∀[e:BasicGeometry]. ∀[A,B,P,Q:Point]. (P-AB-Q ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-opp-side: P-AB-Q,
basic-geometry: BasicGeometry,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
so_apply: x[s],
basic-geometry: BasicGeometry,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
geo-opp-side: P-AB-Q,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-colinear_wf,
geo-between_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
all_wf,
not_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
rename,
setElimination,
because_Cache,
functionEquality,
lambdaEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[A,B,P,Q:Point]. (P-AB-Q \mmember{} \mBbbP{})
Date html generated:
2017_10_02-PM-06_21_28
Last ObjectModification:
2017_08_05-PM-04_16_00
Theory : euclidean!plane!geometry
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