Nuprl Lemma : stable__geo-opp-side
∀[e:BasicGeometry]. ∀[A,B,P,Q:Point]. Stable{P-AB-Q}
Proof
Definitions occuring in Statement :
geo-opp-side: P-AB-Q,
basic-geometry: BasicGeometry,
geo-point: Point,
stable: Stable{P},
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
so_apply: x[s],
basic-geometry: BasicGeometry,
prop: ℙ,
so_lambda: λ2x.t[x],
guard: {T},
subtype_rel: A ⊆r B,
false: False,
implies: P ⇒ Q,
not: ¬A,
and: P ∧ Q,
geo-opp-side: P-AB-Q,
uimplies: b supposing a,
stable: Stable{P},
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-opp-side_wf,
geo-colinear_wf,
not_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,
stable__not,
stable__and
Rules used in proof :
voidElimination,
equalitySymmetry,
equalityTransitivity,
rename,
setElimination,
functionEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
extract_by_obid,
because_Cache,
dependent_functionElimination,
lambdaEquality,
independent_pairEquality,
productElimination,
hypothesisEquality,
thin,
isectElimination,
isect_memberEquality,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
productEquality
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[A,B,P,Q:Point]. Stable\{P-AB-Q\}
Date html generated:
2017_10_02-PM-06_21_55
Last ObjectModification:
2017_08_05-PM-04_16_13
Theory : euclidean!plane!geometry
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