Nuprl Lemma : sq_stable_euclidean-axioms
∀e:EuclideanStructure. SqStable(euclidean-axioms(e))
Proof
Definitions occuring in Statement :
euclidean-axioms: euclidean-axioms(e),
euclidean-structure: EuclideanStructure,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
euclidean-axioms: euclidean-axioms(e),
let: let,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
and: P ∧ Q,
uimplies: b supposing a,
cand: A c∧ B,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
top: Top,
sq_stable: SqStable(P),
not: ¬A,
false: False
Lemmas referenced :
sq_stable__and,
uall_wf,
eu-point_wf,
eu-congruent_wf,
isect_wf,
equal_wf,
not_wf,
eu-between-eq_wf,
eu-extend_wf,
eu-between_wf,
eu-colinear_wf,
eu-inner-pasch_wf,
eu-middle_wf,
and_wf,
eu-line-circle_wf,
pi1_wf_top,
subtype_rel_product,
top_wf,
pi2_wf,
sq_stable__uall,
sq_stable__eu-congruent,
sq_stable__equal,
squash_wf,
sq_stable__eu-between-eq,
set_wf,
sq_stable__not,
sq_stable__eu-between,
sq_stable__colinear,
euclidean-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
isect_memberEquality,
productEquality,
because_Cache,
setEquality,
setElimination,
rename,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
applyEquality,
independent_isectElimination,
voidElimination,
voidEquality,
equalityEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
isectEquality,
isect_memberFormation,
introduction,
axiomEquality
Latex:
\mforall{}e:EuclideanStructure. SqStable(euclidean-axioms(e))
Date html generated:
2016_05_18-AM-06_33_32
Last ObjectModification:
2015_12_28-AM-09_29_03
Theory : euclidean!geometry
Home
Index