Nuprl Lemma : fun-sep-co-trans
∀[A:Type]. ∀ss:SeparationSpace. ∀f,g,h:A ⟶ Point. (fun-sep(ss;A;f;g) ⇒ (fun-sep(ss;A;f;h) ∨ fun-sep(ss;A;g;h)))
Proof
Definitions occuring in Statement :
fun-sep: fun-sep(ss;A;f;g),
ss-point: Point,
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
guard: {T},
prop: ℙ,
or: P ∨ Q,
member: t ∈ T,
exists: ∃x:A. B[x],
fun-sep: fun-sep(ss;A;f;g),
implies: P ⇒ Q,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x]
Lemmas referenced :
separation-space_wf,
ss-point_wf,
fun-sep_wf,
ss-sep_wf,
ss-sep-or
Rules used in proof :
universeEquality,
functionEquality,
inrFormation,
sqequalRule,
isectElimination,
dependent_pairFormation,
inlFormation,
unionElimination,
hypothesis,
independent_functionElimination,
cumulativity,
functionExtensionality,
applyEquality,
hypothesisEquality,
dependent_functionElimination,
extract_by_obid,
introduction,
cut,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:Type]
\mforall{}ss:SeparationSpace. \mforall{}f,g,h:A {}\mrightarrow{} Point.
(fun-sep(ss;A;f;g) {}\mRightarrow{} (fun-sep(ss;A;f;h) \mvee{} fun-sep(ss;A;g;h)))
Date html generated:
2016_11_08-AM-09_11_52
Last ObjectModification:
2016_11_02-AM-10_37_12
Theory : inner!product!spaces
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