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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