Nuprl Lemma : injective-quotient_wf
∀[T,S:Type]. ∀[f:T ⟶ S]. (T//x.f[x] ∈ Type)
Proof
Definitions occuring in Statement :
injective-quotient: T//x.f[x],
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
injective-quotient: T//x.f[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s],
so_apply: x[s1;s2],
uimplies: b supposing a,
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
prop: ℙ,
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
quotient_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
applyEquality,
functionExtensionality,
because_Cache,
hypothesis,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
universeEquality,
independent_pairFormation,
lambdaFormation
Latex:
\mforall{}[T,S:Type]. \mforall{}[f:T {}\mrightarrow{} S]. (T//x.f[x] \mmember{} Type)
Date html generated:
2016_10_21-AM-09_43_54
Last ObjectModification:
2016_08_08-PM-05_03_59
Theory : quot_1
Home
Index