### 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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