Nuprl Lemma : mk-complete-pgeo_wf
∀[pg:ProjectivePlaneStructure]. ∀[p:Point]. (mk-complete-pgeo(pg;p) ∈ ProjectivePlaneStructureComplete)
Proof
Definitions occuring in Statement :
mk-complete-pgeo: mk-complete-pgeo(pg;p),
projective-plane-structure-complete: ProjectivePlaneStructureComplete,
projective-plane-structure: ProjectivePlaneStructure,
pgeo-point: Point,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
mk-complete-pgeo: mk-complete-pgeo(pg;p),
projective-plane-structure-complete: ProjectivePlaneStructureComplete,
record+: record+,
record-update: r[x := v],
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
sq_type: SQType(T),
guard: {T},
record-select: r.x,
bfalse: ff,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
false: False,
projective-plane-structure: ProjectivePlaneStructure,
eq_atom: x =a y,
prop: ℙ,
or: P ∨ Q,
exists: ∃x:A. B[x],
pgeo-lpsep: a ≠ b,
pgeo-psep: a ≠ b,
pgeo-incident: a I b,
pgeo-lsep: l ≠ m,
pgeo-line: Line,
pgeo-point: Point,
pgeo-plsep: pgeo-plsep(p; a; b),
record: record(x.T[x]),
pgeo-primitives: ProjGeomPrimitives,
pgeo-peq: a ≡ b
Latex:
\mforall{}[pg:ProjectivePlaneStructure]. \mforall{}[p:Point].
(mk-complete-pgeo(pg;p) \mmember{} ProjectivePlaneStructureComplete)
Date html generated:
2020_05_20-AM-10_36_42
Last ObjectModification:
2019_12_03-AM-09_49_31
Theory : euclidean!plane!geometry
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