Nuprl Lemma : pgeo-dual_wf2
∀[pg:BasicProjectivePlane]. (pg* ∈ BasicProjectivePlane)
Proof
Definitions occuring in Statement :
basic-projective-plane: BasicProjectivePlane,
pgeo-dual: pg*,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
basic-projective-plane: BasicProjectivePlane,
basic-pgeo-axioms: BasicProjectiveGeometryAxioms(g),
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False,
pgeo-dual: pg*,
pgeo-incident: a I b,
pgeo-dual-prim: pg*,
mk-pgeo: mk-pgeo(p; ss; por; lor; j; m; p3; l3),
pgeo-plsep: pgeo-plsep(p; a; b),
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
pgeo-point: Point,
pgeo-line: Line,
mk-pgeo-prim: mk-pgeo-prim,
btrue: tt,
pgeo-leq: a ≡ b,
pgeo-peq: a ≡ b,
pgeo-lsep: l ≠ m,
pgeo-psep: a ≠ b,
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
pgeo-dual_wf,
rec_select_update_lemma,
not_wf,
pgeo-leq_wf,
pgeo-peq_wf,
pgeo-incident_wf,
pgeo-line_wf,
pgeo-point_wf,
basic-pgeo-axioms_wf,
projective-plane-structure_subtype,
basic-projective-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
lambdaFormation,
sqequalRule,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_functionElimination,
productElimination,
independent_pairFormation,
productEquality,
applyEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[pg:BasicProjectivePlane]. (pg* \mmember{} BasicProjectivePlane)
Date html generated:
2019_10_16-PM-02_12_22
Last ObjectModification:
2018_08_02-PM-01_22_03
Theory : euclidean!plane!geometry
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