Nuprl Lemma : sq_stable__geo-Aparallel
∀[g:EuclideanPlane]. ∀l,m:Line. SqStable(l || m)
Proof
Definitions occuring in Statement :
geo-Aparallel: l || m,
geo-line: Line,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
geo-Aparallel: l || m,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
sq_stable: SqStable(P),
implies: P ⇒ Q,
not: ¬A,
false: False,
prop: ℙ
Lemmas referenced :
sq_stable__not,
geo-intersect_wf,
geoline-subtype1,
geo-line_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
squash_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
dependent_functionElimination,
instantiate,
independent_isectElimination,
because_Cache,
lambdaEquality,
voidElimination
Latex:
\mforall{}[g:EuclideanPlane]. \mforall{}l,m:Line. SqStable(l || m)
Date html generated:
2019_10_16-PM-02_41_51
Last ObjectModification:
2018_08_23-PM-02_02_26
Theory : euclidean!plane!geometry
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