Nuprl Lemma : not-lt-and-symm-le
∀[e:BasicGeometry]. ∀[p,q:Length]. (p ≤ q ⇒ q < p ⇒ False)
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-le: p ≤ q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
false: False
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
false: False,
prop: ℙ,
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
geo-lt_wf,
geo-le_wf,
geo-length-type_wf,
basic-geometry_wf,
geo-lt-irrefl,
geo-lt_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
hypothesis,
universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
dependent_functionElimination,
because_Cache,
functionIsTypeImplies,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
voidElimination,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[p,q:Length]. (p \mleq{} q {}\mRightarrow{} q < p {}\mRightarrow{} False)
Date html generated:
2019_10_16-PM-01_19_38
Last ObjectModification:
2018_12_04-PM-03_29_34
Theory : euclidean!plane!geometry
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