Nuprl Lemma : setmem-mk-set
∀T:Type. ∀f:T ⟶ Set{i:l}. ∀t:T. (f t ∈ f"(T))
Proof
Definitions occuring in Statement :
mk-set: f"(T)
,
Set: Set{i:l}
,
setmem: (x ∈ s)
,
all: ∀x:A. B[x]
,
apply: f a
,
function: x:A ⟶ B[x]
,
universe: Type
Definitions unfolded in proof :
prop: ℙ
,
exists: ∃x:A. B[x]
,
top: Top
,
implies: P
⇒ Q
,
rev_implies: P
⇐ Q
,
and: P ∧ Q
,
iff: P
⇐⇒ Q
,
uall: ∀[x:A]. B[x]
,
subtype_rel: A ⊆r B
,
member: t ∈ T
,
all: ∀x:A. B[x]
Lemmas referenced :
Set_wf,
seteq_wf,
seteq_weakening,
item_mk_set_lemma,
dom_mk_set_lemma,
mk-set_wf,
set-subtype-coSet,
setmem-iff
Rules used in proof :
universeEquality,
cumulativity,
functionEquality,
because_Cache,
dependent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
independent_functionElimination,
productElimination,
isectElimination,
sqequalRule,
hypothesis,
hypothesisEquality,
applyEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}T:Type. \mforall{}f:T {}\mrightarrow{} Set\{i:l\}. \mforall{}t:T. (f t \mmember{} f"(T))
Date html generated:
2018_07_29-AM-09_51_58
Last ObjectModification:
2018_07_20-PM-06_22_19
Theory : constructive!set!theory
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