Nuprl Lemma : geo-add-length-implies-eq-zero
∀[e:BasicGeometry]. ∀[x,y:Length]. y = 0 ∈ Length supposing x = x + y ∈ Length
Proof
Definitions occuring in Statement :
geo-add-length: p + q,
geo-zero-length: 0,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
geo-zero-length: 0,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
true: True,
prop: ℙ,
squash: ↓T,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
basic-geometry_wf,
geo-add-length_wf,
geo-zero-length_wf,
geo-add-length-cancel-left,
iff_weakening_equal,
geo-add-length-zero,
geo-length-type_wf,
true_wf,
squash_wf,
equal_wf
Rules used in proof :
because_Cache,
axiomEquality,
isect_memberEquality,
independent_functionElimination,
productElimination,
independent_isectElimination,
baseClosed,
imageMemberEquality,
sqequalRule,
natural_numberEquality,
universeEquality,
equalitySymmetry,
hypothesis,
equalityTransitivity,
hypothesisEquality,
isectElimination,
extract_by_obid,
imageElimination,
sqequalHypSubstitution,
lambdaEquality,
thin,
applyEquality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[x,y:Length]. y = 0 supposing x = x + y
Date html generated:
2017_10_02-PM-06_14_37
Last ObjectModification:
2017_08_05-PM-04_11_16
Theory : euclidean!plane!geometry
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