Nuprl Lemma : geo-lt-irrefl2
∀e:BasicGeometry. ∀p,q,r:Length. (p < q + r ⇒ q + r < p ⇒ False)
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-add-length: p + q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
all: ∀x:A. B[x],
implies: P ⇒ Q,
false: False
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
false: False,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
uimplies: b supposing a
Lemmas referenced :
geo-lt_wf,
geo-add-length_wf,
geo-length-type_wf,
basic-geometry_wf,
geo-le_weakening-lt,
geo-lt-irrefl,
geo-lt_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
inhabitedIsType,
because_Cache,
independent_isectElimination,
voidElimination,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}p,q,r:Length. (p < q + r {}\mRightarrow{} q + r < p {}\mRightarrow{} False)
Date html generated:
2019_10_16-PM-01_19_23
Last ObjectModification:
2019_01_10-AM-08_17_24
Theory : euclidean!plane!geometry
Home
Index