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
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