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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