Nuprl Lemma : per-isect2_quotient
∀[T:Type]. ∀[E1,E2:T ⟶ T ⟶ ℙ].
(x,y:T/per/E1[x;y] ⋂ x,y:T/per/E2[x;y] ≡ x,y:T/per/(E1[x;y] ∧ E2[x;y])) supposing
(EquivRel(T;x,y.E1[x;y]) and
EquivRel(T;x,y.E2[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,
ext-eq: A ≡ B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
and: P ∧ Q,
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 :
isect2_quotient
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalRule,
sqequalReflexivity,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[T:Type]. \mforall{}[E1,E2:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}].
(x,y:T/per/E1[x;y] \mcap{} x,y:T/per/E2[x;y] \mequiv{} x,y:T/per/(E1[x;y] \mwedge{} E2[x;y])) supposing
(EquivRel(T;x,y.E1[x;y]) and
EquivRel(T;x,y.E2[x;y]))
Date html generated:
2019_06_20-PM-00_33_39
Last ObjectModification:
2018_08_21-PM-10_54_13
Theory : per-quotient
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