Nuprl Lemma : per-quotient-squash
∀[T:Type]. ∀[E:T ⟶ T ⟶ ℙ].  x,y:T/per/E[x;y] ≡ x,y:T/per/(↓E[x;y]) 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])
, 
ext-eq: A ≡ B
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
so_apply: x[s1;s2]
, 
squash: ↓T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
per-quotient: x,y:T/per/E[x; y]
, 
quotient: x,y:A//B[x; y]
Lemmas referenced : 
quotient-squash
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalRule, 
sqequalReflexivity, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
hypothesis
Latex:
\mforall{}[T:Type].  \mforall{}[E:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].
    x,y:T/per/E[x;y]  \mequiv{}  x,y:T/per/(\mdownarrow{}E[x;y])  supposing  EquivRel(T;x,y.E[x;y])
Date html generated:
2019_06_20-PM-00_33_34
Last ObjectModification:
2018_08_21-PM-10_54_14
Theory : per-quotient
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