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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