### Nuprl Lemma : transitive-closure_wf

`∀[A:Type]. ∀[R:A ⟶ A ⟶ ℙ].  (TC(R) ∈ A ⟶ A ⟶ ℙ)`

Proof

Definitions occuring in Statement :  transitive-closure: `TC(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` transitive-closure: `TC(R)` subtype_rel: `A ⊆r B` prop: `ℙ` so_lambda: `λ2x.t[x]` and: `P ∧ Q` so_apply: `x[s]`
Lemmas referenced :  set_wf list_wf and_wf rel_path_wf less_than_wf length_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lambdaEquality lemma_by_obid sqequalHypSubstitution isectElimination thin productEquality hypothesisEquality applyEquality hypothesis universeEquality natural_numberEquality because_Cache axiomEquality equalityTransitivity equalitySymmetry functionEquality cumulativity isect_memberEquality

Latex:
\mforall{}[A:Type].  \mforall{}[R:A  {}\mrightarrow{}  A  {}\mrightarrow{}  \mBbbP{}].    (TC(R)  \mmember{}  A  {}\mrightarrow{}  A  {}\mrightarrow{}  \mBbbP{})

Date html generated: 2016_05_14-PM-03_51_07
Last ObjectModification: 2015_12_26-PM-06_58_33

Theory : relations2

Home Index