### 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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