Nuprl Lemma : quotient-bind-ext
∀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,
implies: P ⇒ Q,
cand: A c∧ B
Lemmas referenced :
quotient_wf,
true_wf,
equiv_rel_true,
istype-universe,
quotient-member-eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
sqequalHypSubstitution,
hypothesis,
Error :functionIsType,
Error :universeIsType,
hypothesisEquality,
introduction,
extract_by_obid,
isectElimination,
thin,
sqequalRule,
Error :lambdaEquality_alt,
Error :inhabitedIsType,
independent_isectElimination,
instantiate,
universeEquality,
pointwiseFunctionalityForEquality,
pertypeElimination,
productElimination,
Error :productIsType,
Error :equalityIstype,
sqequalBase,
equalitySymmetry,
because_Cache,
equalityTransitivity,
applyEquality,
dependent_functionElimination,
independent_functionElimination,
baseApply,
closedConclusion,
baseClosed
Latex:
\mforall{}A,B:Type. \mforall{}a:\00D9(A). \mforall{}f:A {}\mrightarrow{} \00D9(B). (f a \mmember{} \00D9(B))
Date html generated:
2019_06_20-PM-00_32_35
Last ObjectModification:
2018_11_24-PM-10_16_15
Theory : quot_1
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