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
Home
Index