Nuprl Lemma : geo-convex_wf
∀[g:BasicGeometry-]. ∀[P:Point ⟶ ℙ]. (IsConvex(x.P[x]) ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-convex: IsConvex(x.P[x]),
basic-geometry-: BasicGeometry-,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
geo-convex: IsConvex(x.P[x]),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
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
Rules used in proof :
isect_memberEquality,
cumulativity,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
universeEquality,
functionExtensionality,
functionEquality,
because_Cache,
lambdaEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g:BasicGeometry-]. \mforall{}[P:Point {}\mrightarrow{} \mBbbP{}]. (IsConvex(x.P[x]) \mmember{} \mBbbP{})
Date html generated:
2017_10_02-PM-06_48_53
Last ObjectModification:
2017_08_08-PM-00_39_33
Theory : euclidean!plane!geometry
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