Nuprl Lemma : quotient-bind-ext2
∀A,B:Type. ∀a:⇃(A). ∀f:A ⟶ ⇃(B).  (f a ∈ ⇃(B))
Proof
Definitions occuring in Statement : 
quotient: x,y:A//B[x; y]
, 
all: ∀x:A. B[x]
, 
true: True
, 
member: t ∈ T
, 
apply: f a
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
uimplies: b supposing a
, 
quotient: x,y:A//B[x; y]
, 
and: P ∧ Q
, 
prop: ℙ
Lemmas referenced : 
eq-in-quot, 
equal-wf-base, 
equiv_rel_true, 
true_wf, 
quotient_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
sqequalHypSubstitution, 
hypothesis, 
functionEquality, 
cumulativity, 
hypothesisEquality, 
lemma_by_obid, 
isectElimination, 
thin, 
sqequalRule, 
lambdaEquality, 
because_Cache, 
independent_isectElimination, 
universeEquality, 
pointwiseFunctionalityForEquality, 
pertypeElimination, 
productElimination, 
productEquality, 
applyEquality, 
functionExtensionality, 
dependent_functionElimination, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}A,B:Type.  \mforall{}a:\00D9(A).  \mforall{}f:A  {}\mrightarrow{}  \00D9(B).    (f  a  \mmember{}  \00D9(B))
Date html generated:
2016_05_14-AM-06_08_48
Last ObjectModification:
2016_05_13-PM-00_10_06
Theory : quot_1
Home
Index