Nuprl Lemma : rel_exp_functionality_wrt_brle

∀n:ℕ. ∀[T:Type]. ∀[R1,R2:T ⟶ T ⟶ ℙ].  ((R1 ≡>{T} R2) ⇒ (R1^n ≡>{T} R2^n))


Proof




Definitions occuring in Statement :  binrel_le: E ≡>{T} E',  rel_exp: R^n,  nat: ℕ,  uall: ∀[x:A]. B[x],  prop: ℙ,  all: ∀x:A. B[x],  implies: P ⇒ Q,  function: x:A ⟶ B[x],  universe: Type
Definitions unfolded in proof :  rel_implies: R1 => R2,  infix_ap: x f y,  binrel_le: E ≡>{T} E'
Lemmas referenced :  rel_exp_functionality_wrt_rel_implies
Rules used in proof :  cut,  lemma_by_obid,  sqequalHypSubstitution,  sqequalSubstitution,  sqequalRule,  sqequalReflexivity,  sqequalTransitivity,  computationStep,  hypothesis

Latex:
\mforall{}n:\mBbbN{}
    \mforall{}[T:Type].  \mforall{}[R1,R2:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    ((R1  \mequiv{}>\{T\}  R2)  {}\mRightarrow{}  (R1\^{}n  \mequiv{}>\{T\}  R2\^{}n))



Date html generated: 2016_05_14-PM-03_55_03
Last ObjectModification: 2015_12_26-PM-06_55_40

Theory : relations2


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