Nuprl Lemma : funset_wf
∀[A,B:coSet{i:l}]. (A ⟶ B ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
funset: A ⟶ B,
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
funset: A ⟶ B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
setmem_wf,
coSet_wf,
Piset_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
cumulativity,
hypothesis,
setEquality,
lambdaEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A,B:coSet\{i:l\}]. (A {}\mrightarrow{} B \mmember{} coSet\{i:l\})
Date html generated:
2018_07_29-AM-10_05_22
Last ObjectModification:
2018_07_18-PM-03_33_43
Theory : constructive!set!theory
Home
Index