Nuprl Lemma : geo-le-cases
∀e:BasicGeometry. ∀[p,q:Length]. (¬¬(p ≤ q ∨ q ≤ p))
Proof
Definitions occuring in Statement :
geo-le: p ≤ q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
or: P ∨ Q
Definitions unfolded in proof :
or: P ∨ Q,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
and: P ∧ Q,
quotient: x,y:A//B[x; y],
prop: ℙ,
geo-length-type: Length,
false: False,
implies: P ⇒ Q,
not: ¬A,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
so_apply: x[s],
basic-geometry: BasicGeometry,
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
cand: A c∧ B,
squash: ↓T,
exists: ∃x:A. B[x],
geo-le: p ≤ q
Lemmas referenced :
geo-length-type_wf,
geo-le_wf,
or_wf,
not_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-eq_wf,
equal-wf-base,
false_wf,
equal_wf,
geo-X_wf,
geo-O_wf,
geo-between_wf,
geo-point_wf,
set_wf,
geo-length-equiv,
subtype_quotient,
geo-sep-O-X,
geo-between-same-side2,
exists_wf,
member_wf,
and_wf
Rules used in proof :
isect_memberEquality,
dependent_functionElimination,
independent_functionElimination,
rename,
setElimination,
lambdaEquality,
equalitySymmetry,
equalityTransitivity,
independent_isectElimination,
instantiate,
applyEquality,
hypothesisEquality,
because_Cache,
isectElimination,
productEquality,
voidElimination,
productElimination,
pertypeElimination,
sqequalRule,
hypothesis,
extract_by_obid,
pointwiseFunctionalityForEquality,
sqequalHypSubstitution,
thin,
cut,
introduction,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
setEquality,
independent_pairFormation,
inrFormation,
baseClosed,
imageMemberEquality,
dependent_set_memberEquality,
dependent_pairFormation,
inlFormation
Latex:
\mforall{}e:BasicGeometry. \mforall{}[p,q:Length]. (\mneg{}\mneg{}(p \mleq{} q \mvee{} q \mleq{} p))
Date html generated:
2017_10_02-PM-06_17_37
Last ObjectModification:
2017_08_05-PM-04_12_43
Theory : euclidean!plane!geometry
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