Nuprl Lemma : sq_stable__geo-line-eq
∀e:EuclideanPlane. ∀m,l:Line. SqStable(l ≡ m)
Proof
Definitions occuring in Statement :
geo-line-eq: l ≡ m,
geo-line: Line,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
geo-line-eq: l ≡ m,
implies: P ⇒ Q,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
geo-line_wf,
geo-line-sep_wf,
stable__not,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-line-eq_wf,
sq_stable__from_stable
Rules used in proof :
dependent_functionElimination,
because_Cache,
independent_functionElimination,
sqequalRule,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:EuclideanPlane. \mforall{}m,l:Line. SqStable(l \mequiv{} m)
Date html generated:
2018_07_29-AM-09_35_43
Last ObjectModification:
2018_06_21-AM-09_05_51
Theory : euclidean!plane!geometry
Home
Index