Nuprl Lemma : mk-pgeo-prim_wf
∀[P,L:Type]. ∀[S:P ⟶ L ⟶ ℙ]. (points=P lines=L plsep=S ∈ ProjGeomPrimitives)
Proof
Definitions occuring in Statement :
mk-pgeo-prim: mk-pgeo-prim,
pgeo-primitives: ProjGeomPrimitives,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mk-pgeo-prim: mk-pgeo-prim,
pgeo-primitives: ProjGeomPrimitives,
pgeo-line: Line,
pgeo-point: Point,
record+: record+,
record-update: r[x := v],
record: record(x.T[x]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
subtype_rel: A ⊆r B,
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,
top: Top,
eq_atom: x =a y,
bfalse: ff,
iff: P ⇐⇒ Q,
not: ¬A,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
eq_atom_wf,
uiff_transitivity,
equal-wf-base,
bool_wf,
assert_wf,
atom_subtype_base,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
rec_select_update_lemma,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependentIntersection_memberEquality,
because_Cache,
functionExtensionality,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
tokenEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
atomEquality,
independent_functionElimination,
productElimination,
independent_isectElimination,
instantiate,
cumulativity,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
impliesFunctionality,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[P,L:Type]. \mforall{}[S:P {}\mrightarrow{} L {}\mrightarrow{} \mBbbP{}]. (points=P lines=L plsep=S \mmember{} ProjGeomPrimitives)
Date html generated:
2018_05_22-PM-00_22_43
Last ObjectModification:
2018_03_30-PM-09_17_26
Theory : euclidean!plane!geometry
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