Nuprl Lemma : es-interface-equality-prior-recursion
∀[Info,T:Type]. ∀[X,Y:EClass(T)].
X = Y ∈ EClass(T)
supposing ∀es:EO+(Info). ∀e:E. ((((X)' es e) = ((Y)' es e) ∈ bag(T)) ⇒ ((X es e) = (Y es e) ∈ bag(T)))
Proof
Definitions occuring in Statement :
es-prior-val: (X)',
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
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 :
in-eclass_wf,
es-prior-interface_wf1,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
es-E-interface_wf,
bool_wf,
eqtt_to_assert,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
es-prior-interface_wf0,
eclass_wf,
eclass-val_wf,
assert_functionality_wrt_uiff,
squash_wf,
true_wf,
es-prior-interface-equal,
es-locl_wf,
or_wf,
single-bag_wf,
eq_int_wf,
bag-size_wf,
es-causl_weakening,
bag_wf,
nat_wf,
es-E-interface-property,
eclass-val_wf2,
es-prior-interface_wf,
assert_of_eq_int,
bag-only_wf2,
single-valued-bag_wf,
less_than_wf,
es-prior-interface-causl,
iff_weakening_equal,
single-valued-bag-if-le1,
le_weakening,
decidable__lt,
false_wf,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
is-prior-interface
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X,Y:EClass(T)].
X = Y supposing \mforall{}es:EO+(Info). \mforall{}e:E. ((((X)' es e) = ((Y)' es e)) {}\mRightarrow{} ((X es e) = (Y es e)))
Date html generated:
2015_07_21-PM-03_24_49
Last ObjectModification:
2015_02_04-PM-06_18_05
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