Nuprl Lemma : subtype_rel-per-set
∀[A:Type]. ∀[B:A ⟶ Type]. (per-set(A;a.B[a]) ⊆r A)
Proof
Definitions occuring in Statement :
per-set: per-set(A;a.B[a]),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
per-set: per-set(A;a.B[a]),
and: P ∧ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
per-set_wf,
equal-wf-base,
and_wf,
equal_wf,
member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
sqequalRule,
axiomEquality,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache,
pointwiseFunctionality,
pertypeElimination,
productElimination,
productEquality,
applyEquality,
dependent_set_memberEquality,
independent_pairFormation,
setElimination,
rename,
setEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. (per-set(A;a.B[a]) \msubseteq{}r A)
Date html generated:
2016_05_13-PM-03_54_30
Last ObjectModification:
2015_12_26-AM-10_40_45
Theory : per!type
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