Nuprl Lemma : per-set-intro
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[a:A]. a ∈ per-set(A;a.B[a]) supposing B[a]
Proof
Definitions occuring in Statement :
per-set: per-set(A;a.B[a]),
uimplies: b supposing a,
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],
uimplies: b supposing a,
member: t ∈ T,
so_apply: x[s]
Lemmas referenced :
per-set-equality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
applyEquality,
hypothesisEquality,
functionEquality,
cumulativity,
universeEquality,
because_Cache,
hypothesis,
equalityTransitivity,
equalitySymmetry,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
independent_isectElimination
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[a:A]. a \mmember{} per-set(A;a.B[a]) supposing B[a]
Date html generated:
2019_06_20-AM-11_30_25
Last ObjectModification:
2018_08_24-PM-01_08_05
Theory : per!type
Home
Index