Nuprl Lemma : mkset_wf
∀[T:Type]. ∀[f:T ⟶ Set{i:l}]. ({f[t] | t ∈ T} ∈ Set{i:l})
Proof
Definitions occuring in Statement :
mkset: {f[t] | t ∈ T},
Set: Set{i:l},
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mkset: {f[t] | t ∈ T},
Set: Set{i:l},
Wsup: Wsup(a;b),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
Wsup_wf,
Set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
universeEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesisEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[f:T {}\mrightarrow{} Set\{i:l\}]. (\{f[t] | t \mmember{} T\} \mmember{} Set\{i:l\})
Date html generated:
2018_05_22-PM-09_47_40
Last ObjectModification:
2018_05_16-PM-01_31_10
Theory : constructive!set!theory
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