Nuprl Lemma : rel_exp_functionality_wrt_breqv
∀n:ℕ. ∀[T:Type]. ∀[R1,R2:T ⟶ T ⟶ ℙ]. ((R1 <≡>{T} R2) ⇒ (R1^n <≡>{T} R2^n))
Proof
Definitions occuring in Statement :
binrel_eqv: 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 :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
guard: {T},
prop: ℙ
Lemmas referenced :
binrel_le_antisymmetry,
rel_exp_wf,
rel_exp_functionality_wrt_brle,
binrel_le_weakening,
binrel_eqv_inversion,
binrel_eqv_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
because_Cache,
functionEquality,
cumulativity,
universeEquality
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_10
Last ObjectModification:
2015_12_26-PM-06_55_34
Theory : relations2
Home
Index