Nuprl Lemma : per-quotient-isect-base2
∀[T:Type]. ∀[E:T ⟶ T ⟶ ℙ].  x,y:T/per/E[x;y] ⋂ Base ⊆r T ⋂ Base supposing EquivRel(T;x,y.E[x;y])
Proof
Definitions occuring in Statement : 
per-quotient: x,y:T/per/E[x; y]
, 
equiv_rel: EquivRel(T;x,y.E[x; y])
, 
isect2: T1 ⋂ T2
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
so_apply: x[s1;s2]
, 
function: x:A ⟶ B[x]
, 
base: Base
, 
universe: Type
Lemmas referenced : 
isect2_wf, 
per-quotient_wf, 
subtype_rel_self, 
subtype_rel_functionality_wrt_iff, 
per-quotient-isect-base, 
ext-eq_weakening, 
equiv_rel_wf
Rules used in proof : 
Error :old_sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
cut, 
lemma_by_obid, 
Error :old_sqequalHypSubstitution, 
isectElimination, 
thin, 
because_Cache, 
sqequalRule, 
lambdaEquality, 
applyEquality, 
hypothesisEquality, 
independent_isectElimination, 
hypothesis, 
isect_memberFormation, 
introduction, 
productElimination, 
axiomEquality, 
cumulativity, 
isect_memberEquality, 
equalityTransitivity, 
equalitySymmetry, 
functionEquality, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[E:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    x,y:T/per/E[x;y]  \mcap{}  Base  \msubseteq{}r  T  \mcap{}  Base  supposing  EquivRel(T;x,y.E[x;y])
Date html generated:
2019_06_20-PM-00_33_35
Last ObjectModification:
2015_02_03-PM-02_32_21
Theory : per-quotient
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