Nuprl Lemma : euclid5_wf
∀[e:BasicGeometry]. (euclid5(e) ∈ ℙ)
Proof
Definitions occuring in Statement :
euclid5: euclid5(e),
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
exists: ∃x:A. B[x],
so_apply: x[s],
and: P ∧ Q,
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
euclid5: euclid5(e),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
exists_wf,
geo-congruent_wf,
geo-colinear_wf,
not_wf,
geo-strict-between_wf,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-point_wf,
all_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
productEquality,
functionEquality,
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{}[e:BasicGeometry]. (euclid5(e) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-00_12_53
Last ObjectModification:
2018_05_14-PM-03_18_45
Theory : euclidean!plane!geometry
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