### Nuprl Lemma : binrel_eqv_inversion

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

Proof

Definitions occuring in Statement :  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'` uall: `∀[x:A]. B[x]` implies: `P `` Q` all: `∀x:A. B[x]` member: `t ∈ T` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` subtype_rel: `A ⊆r B` uimplies: `b supposing a` guard: `{T}` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q`
Lemmas referenced :  all_wf iff_wf iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation hypothesisEquality cut lemma_by_obid sqequalHypSubstitution isectElimination thin lambdaEquality applyEquality hypothesis functionEquality cumulativity universeEquality equalityTransitivity equalitySymmetry independent_isectElimination addLevel productElimination independent_pairFormation impliesFunctionality dependent_functionElimination independent_functionElimination

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

Date html generated: 2016_05_14-PM-03_54_44
Last ObjectModification: 2015_12_26-PM-06_56_05

Theory : relations2

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