Nuprl Lemma : pgeo-line-class_wf
∀[g:ProjectivePlane]. (LineClass ∈ Type)
Proof
Definitions occuring in Statement :
pgeo-line-class: LineClass,
projective-plane: ProjectivePlane,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
pgeo-line-class: LineClass,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
pgeo-leq-equiv,
pgeo-leq_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,
quotient_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
dependent_functionElimination,
because_Cache,
lambdaEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g:ProjectivePlane]. (LineClass \mmember{} Type)
Date html generated:
2018_05_22-PM-00_56_23
Last ObjectModification:
2018_01_03-PM-03_44_19
Theory : euclidean!plane!geometry
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