Nuprl Lemma : pgeo-finite-plane_wf
∀pg:ProjectivePlane. (pgeo-finite-plane(pg) ∈ ℙ)
Proof
Definitions occuring in Statement :
pgeo-finite-plane: pgeo-finite-plane(pg),
projective-plane: ProjectivePlane,
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
cand: A c∧ B,
exists: ∃x:A. B[x],
so_apply: x[s],
nat: ℕ,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
and: P ∧ Q,
prop: ℙ,
pgeo-finite-plane: pgeo-finite-plane(pg),
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-plsep_wf,
decidable_wf,
all_wf,
pgeo-line_wf,
int_seg_wf,
pgeo-primitives_wf,
projective-plane-structure_wf,
projective-plane-structure-complete_wf,
projective-plane_wf,
subtype_rel_transitivity,
projective-plane-subtype,
projective-plane-structure-complete_subtype,
projective-plane-structure_subtype,
pgeo-point_wf,
equipollent_wf,
nat_wf,
exists_wf
Rules used in proof :
productElimination,
because_Cache,
rename,
setElimination,
natural_numberEquality,
independent_isectElimination,
instantiate,
applyEquality,
hypothesisEquality,
lambdaEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
productEquality,
sqequalRule,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}pg:ProjectivePlane. (pgeo-finite-plane(pg) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-00_59_30
Last ObjectModification:
2018_01_10-AM-09_59_56
Theory : euclidean!plane!geometry
Home
Index