Nuprl Lemma : dual-plane_wf
∀[pg:ProjectivePlane]. (dual-plane(pg) ∈ ProjectivePlane)
Proof
Definitions occuring in Statement :
dual-plane: dual-plane(pg),
projective-plane: ProjectivePlane,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
projective-plane: ProjectivePlane,
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
basic-projective-plane: BasicProjectivePlane,
dual-plane: dual-plane(pg),
pgeo-non-trivial-dual-ext,
pi1: fst(t),
sq_exists: ∃x:A [B[x]],
so_apply: x[s],
so_lambda: λ2x.t[x],
basic-pgeo-axioms: BasicProjectiveGeometryAxioms(g),
pgeo-leq: a ≡ b,
pgeo-peq: a ≡ b,
pgeo-incident: a I b,
pgeo-point: Point,
pgeo-line: Line,
pgeo-lsep: l ≠ m,
pgeo-psep: a ≠ b,
pgeo-plsep: pgeo-plsep(p; a; b),
complete-pgeo-dual: complete-pgeo-dual(pg;l),
pgeo-dual: pg*,
mk-complete-pgeo: mk-complete-pgeo(pg;p),
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
pgeo-dual-prim: pg*,
mk-pgeo: mk-pgeo(p; ss; por; lor; j; m; p3; l3),
mk-pgeo-prim: mk-pgeo-prim,
btrue: tt,
implies: P ⇒ Q,
not: ¬A,
false: False,
pgeo-meet: l ∧ m,
pgeo-join: p ∨ q,
triangle-axiom1: triangle-axiom1(g),
triangle-axiom2: triangle-axiom2(g)
Lemmas referenced :
basic-pgeo-axioms_wf,
projective-plane-structure_subtype,
projective-plane-structure-complete_subtype,
subtype_rel_transitivity,
projective-plane-structure-complete_wf,
projective-plane-structure_wf,
pgeo-primitives_wf,
triangle-axiom1_wf,
triangle-axiom2_wf,
projective-plane_wf,
complete-pgeo-dual_wf,
pgeo-leq_wf,
pgeo-line_wf,
sq_exists_wf,
all_wf,
pgeo-non-trivial-dual-ext,
rec_select_update_lemma,
not_wf,
pgeo-peq_wf,
pgeo-incident_wf,
pgeo-point_wf,
pgeo-triangle-axiom1-dual,
pgeo-triangle-axiom2-dual
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
hypothesis,
productEquality,
extract_by_obid,
isectElimination,
hypothesisEquality,
applyEquality,
instantiate,
independent_isectElimination,
sqequalRule,
dependent_functionElimination,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
independent_functionElimination
Latex:
\mforall{}[pg:ProjectivePlane]. (dual-plane(pg) \mmember{} ProjectivePlane)
Date html generated:
2019_10_16-PM-02_12_54
Last ObjectModification:
2018_08_23-PM-02_14_03
Theory : euclidean!plane!geometry
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