Nuprl Lemma : fun-sep-symmetry
∀[A:Type]. ∀ss:SeparationSpace. ∀f,g:A ⟶ Point. (fun-sep(ss;A;f;g) ⇒ fun-sep(ss;A;g;f))
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,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
prop: ℙ,
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-symmetry
Rules used in proof :
universeEquality,
functionEquality,
isectElimination,
hypothesis,
independent_functionElimination,
cumulativity,
functionExtensionality,
applyEquality,
dependent_functionElimination,
extract_by_obid,
introduction,
cut,
hypothesisEquality,
dependent_pairFormation,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:Type]. \mforall{}ss:SeparationSpace. \mforall{}f,g:A {}\mrightarrow{} Point. (fun-sep(ss;A;f;g) {}\mRightarrow{} fun-sep(ss;A;g;f))
Date html generated:
2016_11_08-AM-09_11_49
Last ObjectModification:
2016_11_02-AM-10_34_32
Theory : inner!product!spaces
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