Nuprl Lemma : sq_stable__trans

[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  ((∀x,y:T.  SqStable(R[x;y]))  SqStable(Trans(T;y,x.R[x;y])))


Proof




Definitions occuring in Statement :  trans: Trans(T;x,y.E[x; y]) sq_stable: SqStable(P) uall: [x:A]. B[x] prop: so_apply: x[s1;s2] all: x:A. B[x] implies:  Q function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  trans: Trans(T;x,y.E[x; y]) uall: [x:A]. B[x] implies:  Q member: t ∈ T so_lambda: λ2x.t[x] prop: so_apply: x[s1;s2] so_apply: x[s] all: x:A. B[x] subtype_rel: A ⊆B
Lemmas referenced :  sq_stable__all all_wf sq_stable_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality cumulativity functionEquality applyEquality functionExtensionality hypothesis independent_functionElimination because_Cache universeEquality dependent_functionElimination

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    ((\mforall{}x,y:T.    SqStable(R[x;y]))  {}\mRightarrow{}  SqStable(Trans(T;y,x.R[x;y])))



Date html generated: 2016_10_21-AM-09_42_39
Last ObjectModification: 2016_08_01-PM-09_48_53

Theory : rel_1


Home Index