Nuprl Lemma : first-class-val
∀[Info,A:Type]. ∀[L:EClass(A) List]. ∀[es:EO+(Info)]. ∀[e:E].
(↑e ∈b L[index-of-first X in L.e ∈b X - 1]) ∧ (first-class(L)(e) = L[index-of-first X in L.e ∈b X - 1](e) ∈ A)
supposing ↑e ∈b first-class(L)
Proof
Definitions occuring in Statement :
first-class: first-class(L),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
select: L[n],
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
subtract: n - m,
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
first_index: index-of-first x in L.P[x]
Lemmas :
assert_witness,
assert_wf,
in-eclass_wf,
first-class_wf,
top_wf,
subtype_rel_list,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
es-interface-subtype_rel2,
list_wf,
event-ordering+_wf,
list_induction,
reduce_nil_lemma,
isempty_lemma,
false_wf,
reduce_cons_lemma,
is-first-class2,
select_wf,
decidable__le,
not-le-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,
first_index_bounds,
length_wf,
eclass-val_wf,
all_wf,
cond-class_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
is-cond-class,
cond-class-val,
iff_weakening_equal,
iff_imp_equal_bool,
btrue_wf,
true_wf,
uiff_transitivity,
equal-wf-T-base,
bnot_wf,
not_wf,
assert_of_bnot,
bool_cases,
first_index_cons,
lt_int_wf,
first_index_wf,
assert_of_lt_int,
nat_wf,
less_than_wf,
subtract_wf,
le_int_wf,
assert_of_le_int,
le_wf,
select-cons,
int_subtype_base
\mforall{}[Info,A:Type]. \mforall{}[L:EClass(A) List]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(\muparrow{}e \mmember{}\msubb{} L[index-of-first X in L.e \mmember{}\msubb{} X - 1])
\mwedge{} (first-class(L)(e) = L[index-of-first X in L.e \mmember{}\msubb{} X - 1](e))
supposing \muparrow{}e \mmember{}\msubb{} first-class(L)
Date html generated:
2015_07_17-PM-00_50_57
Last ObjectModification:
2015_02_04-PM-05_32_17
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