Nuprl Lemma : geo-lt-irrefl
∀[e:BasicGeometry]. ∀[p:Length]. False supposing p < p
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
false: False
Definitions unfolded in proof :
prop: ℙ,
and: P ∧ Q,
exists: ∃x:A. B[x],
geo-lt: p < q,
false: False,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
true: True,
basic-geometry: BasicGeometry,
squash: ↓T,
geo-zero-length: 0,
not: ¬A,
geo-eq: a ≡ b,
uiff: uiff(P;Q),
all: ∀x:A. B[x]
Lemmas referenced :
basic-geometry_wf,
geo-length-type_wf,
geo-lt_wf,
iff_weakening_equal,
geo-add-length-zero,
geo-mk-seg_wf,
geo-length_wf,
geo-add-length_wf,
true_wf,
squash_wf,
geo-le_wf,
geo-zero-length_wf,
geo-add-length-cancel-left-le,
geo-zero-length-iff,
geo-le-zero
Rules used in proof :
voidElimination,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
hypothesisEquality,
isectElimination,
extract_by_obid,
because_Cache,
sqequalRule,
hypothesis,
thin,
productElimination,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
independent_isectElimination,
universeEquality,
baseClosed,
imageMemberEquality,
natural_numberEquality,
rename,
setElimination,
imageElimination,
lambdaEquality,
applyEquality,
dependent_functionElimination
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[p:Length]. False supposing p < p
Date html generated:
2017_10_02-PM-06_18_53
Last ObjectModification:
2017_08_05-PM-04_13_28
Theory : euclidean!plane!geometry
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