Nuprl Lemma : euclidean-axioms_wf
∀[e:EuclideanStructure]. (euclidean-axioms(e) ∈ ℙ)
Proof
Definitions occuring in Statement :
euclidean-axioms: euclidean-axioms(e),
euclidean-structure: EuclideanStructure,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
euclidean-axioms: euclidean-axioms(e),
let: let,
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
cand: A c∧ B,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
euclidean-structure_wf,
pi2_wf,
top_wf,
subtype_rel_product,
pi1_wf_top,
eu-line-circle_wf,
and_wf,
eu-middle_wf,
eu-inner-pasch_wf,
eu-colinear_wf,
eu-between_wf,
eu-extend_wf,
eu-between-eq_wf,
not_wf,
equal_wf,
isect_wf,
eu-congruent_wf,
eu-point_wf,
uall_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
setEquality,
lambdaFormation,
setElimination,
rename,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
applyEquality,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
equalityEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
isectEquality,
axiomEquality
Latex:
\mforall{}[e:EuclideanStructure]. (euclidean-axioms(e) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-06_33_30
Last ObjectModification:
2016_01_12-PM-02_03_37
Theory : euclidean!geometry
Home
Index