### Nuprl Lemma : rel-confluent_wf

`∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  (rel-confluent(T;x,y.R[x;y]) ∈ ℙ)`

Proof

Definitions occuring in Statement :  rel-confluent: `rel-confluent(T;x,y.R[x; y])` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s1;s2]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` rel-confluent: `rel-confluent(T;x,y.R[x; y])` prop: `ℙ` all: `∀x:A. B[x]` implies: `P `` Q` so_apply: `x[s1;s2]` exists: `∃x:A. B[x]` and: `P ∧ Q` subtype_rel: `A ⊆r B`
Lemmas referenced :  subtype_rel_self istype-universe
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt introduction cut sqequalRule functionEquality hypothesisEquality applyEquality productEquality hypothesis thin instantiate extract_by_obid sqequalHypSubstitution isectElimination because_Cache axiomEquality equalityTransitivity equalitySymmetry functionIsType universeIsType universeEquality isect_memberEquality_alt isectIsTypeImplies inhabitedIsType

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (rel-confluent(T;x,y.R[x;y])  \mmember{}  \mBbbP{})

Date html generated: 2019_10_15-AM-10_24_35
Last ObjectModification: 2019_08_16-PM-02_33_13

Theory : relations2

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