### Nuprl Lemma : es-interface-equality-recursion

`∀[Info,A:Type]. ∀[X,Y:EClass(A)].`
`  X = Y ∈ EClass(A) `
`  supposing ∀es:EO+(Info). ∀e:E.`
`              ((∀e':E. ((e' < e) `` ((X es e') = (Y es e') ∈ bag(A)))) `` ((X es e) = (Y es e) ∈ bag(A)))`

Proof

Definitions occuring in Statement :  eclass: `EClass(A[eo; e])` event-ordering+: `EO+(Info)` es-causl: `(e < e')` es-E: `E` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` apply: `f a` universe: `Type` equal: `s = t ∈ T` bag: `bag(T)`
Lemmas :  es-E_wf event-ordering+_subtype all_wf event-ordering+_wf es-causl_wf bag_wf eclass_wf es-causl-swellfnd nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf int_seg_wf int_seg_subtype-nat decidable__le subtract_wf false_wf not-ge-2 less-iff-le condition-implies-le minus-one-mul zero-add minus-add minus-minus add-associates add-swap add-commutes add_functionality_wrt_le add-zero le-add-cancel decidable__equal_int subtype_rel-int_seg le_weakening int_seg_properties le_wf nat_wf zero-le-nat lelt_wf equal_wf decidable__lt not-equal-2 le-add-cancel-alt not-le-2 sq_stable__le add-mul-special zero-mul
\mforall{}[Info,A:Type].  \mforall{}[X,Y:EClass(A)].
X  =  Y
supposing  \mforall{}es:EO+(Info).  \mforall{}e:E.
((\mforall{}e':E.  ((e'  <  e)  {}\mRightarrow{}  ((X  es  e')  =  (Y  es  e'))))  {}\mRightarrow{}  ((X  es  e)  =  (Y  es  e)))

Date html generated: 2015_07_17-PM-01_05_56
Last ObjectModification: 2015_01_27-PM-10_39_13

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