Nuprl Lemma : funset_wf2
∀[A,B:Set{i:l}]. (A ⟶ B ∈ Set{i:l})
Proof
Definitions occuring in Statement :
funset: A ⟶ B,
Set: Set{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
funset: A ⟶ B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
set-subtype-coSet,
setmem_wf,
Set_wf,
Piset_wf2
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
applyEquality,
cumulativity,
hypothesis,
setEquality,
lambdaEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A,B:Set\{i:l\}]. (A {}\mrightarrow{} B \mmember{} Set\{i:l\})
Date html generated:
2018_07_29-AM-10_05_26
Last ObjectModification:
2018_07_18-PM-03_33_54
Theory : constructive!set!theory
Home
Index