Nuprl Lemma : fun-ss-eq
∀[ss:SeparationSpace]. ∀[A:Type]. ∀[f,g:A ⟶ Point(ss)]. uiff(f ≡ g;∀a:A. f a ≡ g a)
Proof
Definitions occuring in Statement :
fun-ss: A ⟶ ss,
ss-eq: x ≡ y,
ss-point: Point(ss),
separation-space: SeparationSpace,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
all: ∀x:A. B[x],
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
top: Top,
member: t ∈ T,
ss-eq: x ≡ y,
uall: ∀[x:A]. B[x]
Lemmas referenced :
separation-space_wf,
ss-point_wf,
all_wf,
exists_wf,
not_wf,
ss-sep_wf,
fun-ss-sep
Rules used in proof :
productElimination,
universeEquality,
functionEquality,
because_Cache,
dependent_functionElimination,
lambdaEquality,
applyEquality,
hypothesisEquality,
dependent_pairFormation,
independent_functionElimination,
lambdaFormation,
independent_pairFormation,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
sqequalRule,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[ss:SeparationSpace]. \mforall{}[A:Type]. \mforall{}[f,g:A {}\mrightarrow{} Point(ss)]. uiff(f \mequiv{} g;\mforall{}a:A. f a \mequiv{} g a)
Date html generated:
2018_07_29-AM-10_11_04
Last ObjectModification:
2018_07_03-PM-05_47_58
Theory : constructive!algebra
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