Nuprl Lemma : t-sqle_wf

[T:Type]. ∀[a,b:T].  (t-sqle(T;a;b) ∈ ℙ)


Proof




Definitions occuring in Statement :  t-sqle: t-sqle(T;a;b) uall: [x:A]. B[x] prop: member: t ∈ T universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T t-sqle: t-sqle(T;a;b) subtype_rel: A ⊆B so_lambda: λ2x.t[x] per-class: per-class(T;a) so_apply: x[s]
Lemmas referenced :  squash_wf exists_wf per-class_wf subtype_rel_b-union-right base_wf sqle_wf_base
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality applyEquality hypothesis because_Cache lambdaEquality setElimination rename axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[a,b:T].    (t-sqle(T;a;b)  \mmember{}  \mBbbP{})



Date html generated: 2016_05_13-PM-04_12_46
Last ObjectModification: 2015_12_26-AM-11_11_55

Theory : subtype_1


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