### Nuprl Lemma : binrel_ap_functionality_wrt_breqv

`∀[T:Type]. ∀[r,r':T ⟶ T ⟶ ℙ].  ∀a,b:T.  ((r <≡>{T} r') `` (a [r] b `⇐⇒` a [r'] b))`

Proof

Definitions occuring in Statement :  binrel_ap: `a [r] b` binrel_eqv: `E <≡>{T} E'` uall: `∀[x:A]. B[x]` prop: `ℙ` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` implies: `P `` Q` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  binrel_ap: `a [r] b` binrel_eqv: `E <≡>{T} E'` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` member: `t ∈ T` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  all_wf iff_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality applyEquality hypothesis functionEquality cumulativity universeEquality dependent_functionElimination

Latex:
\mforall{}[T:Type].  \mforall{}[r,r':T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    \mforall{}a,b:T.    ((r  <\mequiv{}>\{T\}  r')  {}\mRightarrow{}  (a  [r]  b  \mLeftarrow{}{}\mRightarrow{}  a  [r']  b))

Date html generated: 2016_05_15-PM-00_00_40
Last ObjectModification: 2015_12_26-PM-11_26_35

Theory : gen_algebra_1

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