Nuprl Lemma : geo-le-zero
∀e:BasicGeometry. ∀[p:Length]. uiff(p ≤ 0;p = 0 ∈ Length)
Proof
Definitions occuring in Statement :
geo-le: p ≤ q,
geo-zero-length: 0,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
squash: ↓T,
geo-le: p ≤ q,
prop: ℙ,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
basic-geometry: BasicGeometry,
geo-zero-length: 0,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
true: True
Lemmas referenced :
basic-geometry_wf,
geo-length-type_wf,
equal_wf,
geo-zero-length_wf,
geo-le_wf,
geo-X_wf,
geo-length-null-segment,
iff_weakening_equal,
true_wf,
squash_wf,
geo-mk-seg_wf,
geo-length_wf,
uiff_wf,
geo-le-null-segment
Rules used in proof :
baseClosed,
imageMemberEquality,
imageElimination,
equalitySymmetry,
equalityTransitivity,
extract_by_obid,
hypothesis,
axiomEquality,
hypothesisEquality,
isectElimination,
isect_memberEquality,
independent_pairEquality,
thin,
productElimination,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
rename,
setElimination,
dependent_functionElimination,
because_Cache,
independent_functionElimination,
universeEquality,
lambdaEquality,
applyEquality,
independent_isectElimination,
independent_pairFormation,
addLevel,
cumulativity,
natural_numberEquality
Latex:
\mforall{}e:BasicGeometry. \mforall{}[p:Length]. uiff(p \mleq{} 0;p = 0)
Date html generated:
2017_10_02-PM-06_13_39
Last ObjectModification:
2017_08_05-PM-04_10_48
Theory : euclidean!plane!geometry
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