Nuprl Lemma : stable__geo-le
∀e:BasicGeometry. ∀x,y:Length. Stable{x ≤ y}
Proof
Definitions occuring in Statement :
geo-le: p ≤ q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
stable: Stable{P},
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
stable: Stable{P},
uimplies: b supposing a,
member: t ∈ T,
geo-length-type: Length,
uall: ∀[x:A]. B[x],
prop: ℙ,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
subtype_rel: A ⊆r B,
guard: {T},
implies: P ⇒ Q,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
geo-le: p ≤ q,
squash: ↓T,
not: ¬A,
false: False,
exists: ∃x:A. B[x],
cand: A c∧ B,
iff: P ⇐⇒ Q
Lemmas referenced :
geo-le_wf,
subtype_rel_self,
geo-length-type_wf,
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,
geo-point_wf,
geo-between_wf,
geo-O_wf,
geo-X_wf,
istype-void,
subtype-geo-length-type,
member_wf,
equal_wf,
stable__geo-between,
squash_wf,
geo-between_functionality,
geo-eq_weakening
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,
productElimination,
equalityTransitivity,
equalitySymmetry,
applyEquality,
independent_functionElimination,
productIsType,
equalityIsType4,
because_Cache,
universeIsType,
instantiate,
independent_isectElimination,
applyLambdaEquality,
setElimination,
rename,
setIsType,
dependent_functionElimination,
imageElimination,
imageMemberEquality,
baseClosed,
functionIsType,
inhabitedIsType,
equalityIsType1,
dependent_pairFormation_alt,
independent_pairFormation,
productEquality,
setEquality,
voidElimination
Latex:
\mforall{}e:BasicGeometry. \mforall{}x,y:Length. Stable\{x \mleq{} y\}
Date html generated:
2019_10_16-PM-01_18_33
Last ObjectModification:
2018_11_12-PM-03_54_42
Theory : euclidean!plane!geometry
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