Nuprl Lemma : rel_plus_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ Type]. (R+ ∈ T ⟶ T ⟶ Type)
Proof
Definitions occuring in Statement :
rel_plus: R+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
rel_plus: R+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
infix_ap: x f y,
subtype_rel: A ⊆r B,
prop: ℙ,
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
exists_wf,
nat_plus_wf,
rel_exp_wf,
nat_plus_subtype_nat
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} Type]. (R\msupplus{} \mmember{} T {}\mrightarrow{} T {}\mrightarrow{} Type)
Date html generated:
2016_05_14-PM-03_51_27
Last ObjectModification:
2015_12_26-PM-06_57_30
Theory : relations2
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