Nuprl Lemma : Playfair-axiom_wf
∀g:EuclideanPlane. (Playfair-axiom(g) ∈ ℙ)
Proof
Definitions occuring in Statement :
Playfair-axiom: Playfair-axiom(e),
euclidean-plane: EuclideanPlane,
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
Playfair-axiom: Playfair-axiom(e),
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
so_apply: x[s]
Lemmas referenced :
all_wf,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-line_wf,
geo-incident_wf,
geoline-subtype1,
geo-Aparallel_wf,
geo-line-eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
lambdaEquality,
dependent_functionElimination,
because_Cache,
functionEquality,
productEquality,
productElimination
Latex:
\mforall{}g:EuclideanPlane. (Playfair-axiom(g) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-01_08_19
Last ObjectModification:
2018_05_11-PM-10_50_06
Theory : euclidean!plane!geometry
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