Nuprl Lemma : respects-equality-quotient1

[X,T:Type]. ∀[E:T ⟶ T ⟶ ℙ].
  (respects-equality(X;x,y:T//E[x;y])) supposing (respects-equality(X;T) and EquivRel(T;x,y.E[x;y]))


Definitions occuring in Statement :  equiv_rel: EquivRel(T;x,y.E[x; y]) quotient: x,y:A//B[x; y] uimplies: supposing a respects-equality: respects-equality(S;T) 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] uimplies: supposing a respects-equality: respects-equality(S;T) all: x:A. B[x] implies:  Q member: t ∈ T so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] prop: quotient: x,y:A//B[x; y] and: P ∧ Q cand: c∧ B subtype_rel: A ⊆B
Lemmas referenced :  quotient_wf istype-base respects-equality_wf equiv_rel_wf istype-universe subtype_rel_self change-equality-type subtype_quotient
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  Error :lambdaFormation_alt,  sqequalRule Error :equalityIstype,  Error :universeIsType,  cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality Error :lambdaEquality_alt,  applyEquality Error :inhabitedIsType,  independent_isectElimination hypothesis because_Cache sqequalBase equalitySymmetry Error :functionIsType,  universeEquality instantiate pertypeElimination promote_hyp productElimination Error :productIsType,  equalityTransitivity independent_functionElimination dependent_functionElimination

\mforall{}[X,T:Type].  \mforall{}[E:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].
    (respects-equality(X;x,y:T//E[x;y]))  supposing  (respects-equality(X;T)  and  EquivRel(T;x,y.E[x;y]))

Date html generated: 2019_06_20-PM-00_32_26
Last ObjectModification: 2018_12_13-PM-04_09_24

Theory : quot_1

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