Nuprl Lemma : injective-quotient-typing
∀[T,S:Type]. ∀[f:T ⟶ S]. (f ∈ T//x.f[x] ⟶ S)
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,
so_lambda: λ2x.t[x],
so_apply: x[s],
injective-quotient: T//x.f[x],
quotient: x,y:A//B[x; y],
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
injective-quotient_wf,
equal-wf-base,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality,
pointwiseFunctionalityForEquality,
pertypeElimination,
productElimination,
productEquality
Latex:
\mforall{}[T,S:Type]. \mforall{}[f:T {}\mrightarrow{} S]. (f \mmember{} T//x.f[x] {}\mrightarrow{} S)
Date html generated:
2017_04_14-AM-07_40_08
Last ObjectModification:
2017_02_27-PM-03_11_23
Theory : quot_1
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