Nuprl Lemma : per-set_wf
∀[A:Type]. ∀[B:A ⟶ Type]. (per-set(A;a.B[a]) ∈ Type)
Proof
Definitions occuring in Statement :
per-set: per-set(A;a.B[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],
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
so_apply: x[s],
cand: A c∧ B,
per-set: per-set(A;a.B[a])
Lemmas referenced :
equal-wf-base,
and_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
productEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesis,
applyEquality,
functionExtensionality,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_pairFormation,
dependent_set_memberEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
hyp_replacement,
Error :applyLambdaEquality,
sqequalRule,
pertypeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. (per-set(A;a.B[a]) \mmember{} Type)
Date html generated:
2016_10_21-AM-09_39_40
Last ObjectModification:
2016_07_12-AM-05_01_32
Theory : per!type
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