Nuprl Lemma : geo-le_weakening
∀[e:BasicGeometry]. ∀[p,q:Length]. p ≤ q supposing p = q ∈ Length
Proof
Definitions occuring in Statement :
geo-le: p ≤ q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
geo-length-type: Length,
prop: ℙ,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
subtype_rel: A ⊆r B,
guard: {T},
squash: ↓T,
all: ∀x:A. B[x],
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane
Lemmas referenced :
sq_stable__geo-le,
subtype-geo-length-type,
geo-le_wf,
equal-wf-base,
geo-eq_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
basic-geometry-subtype,
subtype_rel_transitivity,
basic-geometry_wf,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
equal_wf,
geo-length-type_wf,
geo-between-trivial,
geo-X_wf,
geo-point_wf,
geo-between_wf,
geo-O_wf,
geo-le_witness
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
pointwiseFunctionalityForEquality,
sqequalRule,
pertypeElimination,
productElimination,
productEquality,
because_Cache,
applyEquality,
instantiate,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
setElimination,
rename,
hyp_replacement,
applyLambdaEquality,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
setEquality
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[p,q:Length]. p \mleq{} q supposing p = q
Date html generated:
2017_10_02-PM-04_52_22
Last ObjectModification:
2017_08_17-PM-01_34_41
Theory : euclidean!plane!geometry
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