Nuprl Lemma : rel_star_functionality_wrt_breqv
∀[T:Type]. ∀[R1,R2:T ⟶ T ⟶ ℙ]. ((R1 <≡>{T} R2) ⇒ ((R1^*) <≡>{T} (R2^*)))
Proof
Definitions occuring in Statement :
binrel_eqv: E <≡>{T} E',
rel_star: R^*,
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
guard: {T},
prop: ℙ
Lemmas referenced :
binrel_le_antisymmetry,
rel_star_wf,
rel_star_functionality_wrt_brle,
binrel_le_weakening,
binrel_eqv_inversion,
binrel_eqv_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R1,R2:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. ((R1 <\mequiv{}>\{T\} R2) {}\mRightarrow{} (rel\_star(T; R1) <\mequiv{}>\{T\} rel\_star(T; R2)))
Date html generated:
2016_05_14-PM-03_55_07
Last ObjectModification:
2015_12_26-PM-06_55_36
Theory : relations2
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