Nuprl Lemma : pgeo-order_wf
∀pg:ProjectivePlane. ∀n:ℕ. (order(pg) = n ∈ ℙ)
Proof
Definitions occuring in Statement :
pgeo-order: order(pg) = n,
projective-plane: ProjectivePlane,
nat: ℕ,
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
nat: ℕ,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
prop: ℙ,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
pgeo-order: order(pg) = n,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
nat_wf,
int_seg_wf,
pgeo-order-equiv_rel,
pgeo-peq_wf,
pgeo-incident_wf,
pgeo-point_wf,
quotient_wf,
equipollent_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-line_wf,
all_wf
Rules used in proof :
addEquality,
natural_numberEquality,
dependent_functionElimination,
rename,
setElimination,
because_Cache,
setEquality,
lambdaEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
sqequalRule,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}pg:ProjectivePlane. \mforall{}n:\mBbbN{}. (order(pg) = n \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-00_58_16
Last ObjectModification:
2018_01_10-AM-10_35_27
Theory : euclidean!plane!geometry
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