Nuprl Lemma : geo-add-length-cancel-right-lt
∀[e:BasicGeometry]. ∀[x,y,z:Length]. (z + x < y + x ⇒ z < y)
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-add-length: p + q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q
Lemmas referenced :
geo-add-length-comm,
geo-lt_wf,
squash_wf,
true_wf,
geo-add-length_wf,
subtype_rel_self,
iff_weakening_equal,
geo-add-length-cancel-left-lt,
geo-length-type_wf,
basic-geometry_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeIsType,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
inhabitedIsType
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[x,y,z:Length]. (z + x < y + x {}\mRightarrow{} z < y)
Date html generated:
2019_10_16-PM-01_20_01
Last ObjectModification:
2019_01_30-PM-01_20_06
Theory : euclidean!plane!geometry
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