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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