Nuprl Lemma : PlayfairPP_wf
∀[e:EuclideanPlane]. (PlayfairPP(e) ∈ ℙ)
Proof
Definitions occuring in Statement :
PlayfairPP: PlayfairPP(eu),
euclidean-plane: EuclideanPlane,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
PlayfairPP: PlayfairPP(eu),
prop: ℙ,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
implies: P ⇒ Q,
and: P ∧ Q
Lemmas referenced :
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-parallel-points_wf,
geo-colinear_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
because_Cache,
productEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType
Latex:
\mforall{}[e:EuclideanPlane]. (PlayfairPP(e) \mmember{} \mBbbP{})
Date html generated:
2019_10_16-PM-01_48_09
Last ObjectModification:
2019_06_19-PM-01_48_12
Theory : euclidean!plane!geometry
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