Nuprl Lemma : pgeo-dual_wf
∀[pg:ProjectivePlaneStructure]. (pg* ∈ ProjectivePlaneStructure)
Proof
Definitions occuring in Statement :
pgeo-dual: pg*,
projective-plane-structure: ProjectivePlaneStructure,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
projective-plane-structure: ProjectivePlaneStructure,
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
all: ∀x:A. B[x],
prop: ℙ,
or: P ∨ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
and: P ∧ Q,
pgeo-dual: pg*,
pgeo-point: Point,
pgeo-dual-prim: pg*,
mk-pgeo-prim: mk-pgeo-prim,
record-update: r[x := v],
bfalse: ff,
pgeo-line: Line,
uimplies: b supposing a,
squash: ↓T,
pgeo-plsep: pgeo-plsep(p; a; b),
true: True,
pgeo-lsep: l ≠ m,
pgeo-incident: a I b,
top: Top,
pgeo-psep: a ≠ b,
pgeo-lpsep: a ≠ b
Lemmas referenced :
subtype_rel_self,
pgeo-line_wf,
pgeo-point_wf,
sq_stable_wf,
pgeo-plsep_wf,
pgeo-lsep_wf,
pgeo-lpsep_wf,
pgeo-psep_wf,
pgeo-incident_wf,
mk-pgeo_wf,
pgeo-dual-prim_wf,
subtype_rel-equal,
rec_select_update_lemma,
istype-void,
projective-plane-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
hypothesisEquality,
sqequalHypSubstitution,
dependentIntersectionElimination,
sqequalRule,
dependentIntersectionEqElimination,
thin,
hypothesis,
applyEquality,
tokenEquality,
extract_by_obid,
isectElimination,
functionEquality,
setEquality,
unionEquality,
setElimination,
rename,
productEquality,
lambdaEquality_alt,
functionExtensionality,
independent_isectElimination,
imageElimination,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeIsType,
dependent_functionElimination,
isect_memberEquality_alt,
voidElimination,
equalityTransitivity,
equalitySymmetry,
axiomEquality
Latex:
\mforall{}[pg:ProjectivePlaneStructure]. (pg* \mmember{} ProjectivePlaneStructure)
Date html generated:
2019_10_16-PM-02_11_32
Last ObjectModification:
2018_12_13-PM-01_38_48
Theory : euclidean!plane!geometry
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