Nuprl Lemma : geo-le-add1
∀e:BasicGeometry. ∀[p,q:Length]. p ≤ p + q
Proof
Definitions occuring in Statement :
geo-le: p ≤ q,
geo-add-length: p + q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
geo-length-type: Length,
prop: ℙ,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
subtype_rel: A ⊆r B,
guard: {T},
geo-le: p ≤ q,
exists: ∃x:A. B[x],
cand: A c∧ B,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
respects-equality: respects-equality(S;T),
squash: ↓T,
geo-add-length: p + q,
sq_stable: SqStable(P),
basic-geometry-: BasicGeometry-
Lemmas referenced :
geo-le_wf,
geo-add-length_wf,
subtype_rel_self,
geo-length-type_wf,
subtype-geo-length-type,
geo-add-length_wf1,
respects-equality-quotient1,
geo-point_wf,
geo-between_wf,
geo-O_wf,
geo-X_wf,
geo-eq_wf,
geo-length-equiv,
respects-equality-sets,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
basic-geometry-subtype,
subtype_rel_transitivity,
respects-equality-trivial,
basic-geometry_wf,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-extend-property,
subtype_rel_sets_simple,
geo-sep_wf,
geo-Op-sep,
geo-extend_wf,
geo-congruent_wf,
sq_stable__geo-between,
geo-between-symmetry,
geo-between-inner-trans,
geo-between-exchange3,
basic-geometry-_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
hypothesis,
pertypeElimination,
promote_hyp,
productElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyEquality,
dependent_pairFormation_alt,
independent_pairFormation,
productIsType,
equalityIstype,
setEquality,
dependent_functionElimination,
setElimination,
rename,
lambdaEquality_alt,
inhabitedIsType,
independent_isectElimination,
universeIsType,
instantiate,
independent_functionElimination,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
sqequalBase,
setIsType,
imageElimination,
isect_memberEquality_alt,
isectIsTypeImplies,
dependent_set_memberEquality_alt
Latex:
\mforall{}e:BasicGeometry. \mforall{}[p,q:Length]. p \mleq{} p + q
Date html generated:
2019_10_16-PM-01_16_31
Last ObjectModification:
2019_01_19-AM-10_02_07
Theory : euclidean!plane!geometry
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