Nuprl Lemma : sq_stable__geo-le
∀[e:BasicGeometry]. ∀[p,q:Length]. SqStable(p ≤ q)
Proof
Definitions occuring in Statement :
geo-le: p ≤ q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
geo-le: p ≤ q,
squash: ↓T,
prop: ℙ,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
subtype-geo-length-type,
squash_wf,
geo-le_wf,
geo-length-type_wf,
basic-geometry_wf,
sq_stable__squash,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
basic-geometry-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-O_wf,
geo-X_wf,
equal_wf,
geo-between_wf,
exists_wf,
geo-point_wf,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
imageElimination,
imageMemberEquality,
baseClosed,
isect_memberEquality,
because_Cache,
setElimination,
rename,
applyEquality,
instantiate,
independent_isectElimination,
setEquality
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[p,q:Length]. SqStable(p \mleq{} q)
Date html generated:
2017_10_02-PM-04_52_09
Last ObjectModification:
2017_08_17-PM-01_34_16
Theory : euclidean!plane!geometry
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