Nuprl Lemma : subtype_rel_quotient_trivial

[T:Type]. ∀[E:T ⟶ T ⟶ ℙ].  T ⊆(x,y:T//E[x;y]) supposing EquivRel(T;x,y.E[x;y])


Proof




Definitions occuring in Statement :  equiv_rel: EquivRel(T;x,y.E[x; y]) quotient: x,y:A//B[x; y] uimplies: supposing a subtype_rel: A ⊆B uall: [x:A]. B[x] prop: so_apply: x[s1;s2] function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] subtype_rel: A ⊆B prop:
Lemmas referenced :  subtype_quotient equiv_rel_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule lambdaEquality applyEquality independent_isectElimination hypothesis axiomEquality isect_memberEquality because_Cache equalityTransitivity equalitySymmetry functionEquality cumulativity universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[E:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    T  \msubseteq{}r  (x,y:T//E[x;y])  supposing  EquivRel(T;x,y.E[x;y])



Date html generated: 2016_05_14-AM-06_08_06
Last ObjectModification: 2015_12_26-AM-11_48_27

Theory : quot_1


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