Nuprl Lemma : acyclic-rel_wf
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. (acyclic-rel(T;R) ∈ ℙ)
Proof
Definitions occuring in Statement :
acyclic-rel: acyclic-rel(T;R),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
acyclic-rel: acyclic-rel(T;R),
so_lambda: λ2x.t[x],
infix_ap: x f y,
prop: ℙ,
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
all_wf,
not_wf,
rel_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (acyclic-rel(T;R) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-03_53_28
Last ObjectModification:
2015_12_26-PM-06_56_47
Theory : relations2
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