Nuprl Lemma : rel-immediate_functionality_wrt_breqv
∀[T:Type]. ∀[R,Q:T ⟶ T ⟶ ℙ]. ((R <≡>{T} Q) ⇒ (R! <≡>{T} Q!))
Proof
Definitions occuring in Statement :
rel-immediate: R!,
binrel_eqv: E <≡>{T} E',
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
binrel_eqv: E <≡>{T} E'
Lemmas referenced :
rel-immediate_functionality_wrt_iff
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
hypothesis
Latex:
\mforall{}[T:Type]. \mforall{}[R,Q:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. ((R <\mequiv{}>\{T\} Q) {}\mRightarrow{} (R! <\mequiv{}>\{T\} Q!))
Date html generated:
2016_05_15-PM-04_53_36
Last ObjectModification:
2015_12_27-PM-02_31_58
Theory : general
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