Nuprl Lemma : mk-coset_wf
∀[T:Type]. ∀[f:T ⟶ coSet{i:l}]. (mk-coset(T;f) ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
mk-coset: mk-coset(T;f),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
mk-coset: mk-coset(T;f),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
subtype_coSet,
coSet_wf
Rules used in proof :
universeEquality,
because_Cache,
thin,
isectElimination,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
sqequalHypSubstitution,
applyEquality,
hypothesis,
extract_by_obid,
cumulativity,
functionEquality,
hypothesisEquality,
dependent_pairEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[f:T {}\mrightarrow{} coSet\{i:l\}]. (mk-coset(T;f) \mmember{} coSet\{i:l\})
Date html generated:
2018_07_29-AM-09_49_34
Last ObjectModification:
2018_07_10-PM-10_24_48
Theory : constructive!set!theory
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