Nuprl Lemma : rel-preserving_wf
∀[T1,T2:Type]. ∀[R1:T1 ⟶ T1 ⟶ Type]. ∀[R2:T2 ⟶ T2 ⟶ Type]. ∀[f:T2 ⟶ T1]. (λx.f[x]:T2->T1 takes R2 into R1*) ∈ ℙ)
Proof
Definitions occuring in Statement :
rel-preserving: λx.f[x]:T2->T1 takes R2 into R1*),
uall: ∀[x:A]. B[x],
prop: ℙ,
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,
rel-preserving: λx.f[x]:T2->T1 takes R2 into R1*),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
infix_ap: x f y,
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
all_wf,
rel_star_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
applyEquality,
hypothesis,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T1,T2:Type]. \mforall{}[R1:T1 {}\mrightarrow{} T1 {}\mrightarrow{} Type]. \mforall{}[R2:T2 {}\mrightarrow{} T2 {}\mrightarrow{} Type]. \mforall{}[f:T2 {}\mrightarrow{} T1].
(\mlambda{}x.f[x]:T2->T1 takes R2 into R1*) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-05_40_22
Last ObjectModification:
2015_12_27-PM-02_05_46
Theory : general
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