Nuprl Lemma : first-at-filter-interface-predecessors-or
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[T:Type]. ∀[X:EClass(T)]. ∀[P:E(X) ─→ 𝔹]. ∀[Q:E(X) ─→ ℙ]. ∀[n:ℕ+]. ∀[e:E]. ∀[i:Id].
↑e ∈b X supposing e is first@ i s.t. q.((↑q ∈b X) ∧ Q[q]) ∨ (||filter(λe.P[e];≤(X)(q))|| = n ∈ ℤ)
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first-at: e is first@ i s.t. e.P[e],
es-E: E,
Id: Id,
filter: filter(P;l),
length: ||as||,
nat_plus: ℕ+,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
or: P ∨ Q,
and: P ∧ Q,
lambda: λx.A[x],
function: x:A ─→ B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
es-first-at-implies,
assert_wf,
decidable__assert,
in-eclass_wf,
set_wf,
not_wf,
or_wf,
equal_wf,
length_wf,
es-loc_wf,
filter_wf5,
es-interface-predecessors_wf,
l_member_wf,
assert_witness,
es-first-at_wf,
event-ordering+_subtype,
Id_wf,
es-E_wf,
es-interface-subtype_rel2,
event-ordering+_wf,
top_wf,
es-E-interface_wf,
nat_plus_wf,
bool_wf,
eclass_wf,
es-prior-interface_wf1,
subtype_top,
squash_wf,
true_wf,
list_wf,
es-interface-predecessors-general-step,
iff_weakening_equal,
bool_cases,
subtype_base_sq,
bool_subtype_base,
eqtt_to_assert,
eqff_to_assert,
assert_of_bnot,
list_ind_nil_lemma,
filter_cons_lemma,
filter_nil_lemma,
length_of_nil_lemma,
eclass-val_wf2,
es-prior-interface_wf,
append-nil,
subtype_rel_list,
es-loc-prior-interface,
es-prior-interface-causl,
decidable__equal_int,
false_wf,
not-equal-2,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-swap,
add-commutes,
le-add-cancel,
add-associates,
es-locl_wf,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[P:E(X) {}\mrightarrow{} \mBbbB{}]. \mforall{}[Q:E(X) {}\mrightarrow{} \mBbbP{}]. \mforall{}[n:\mBbbN{}\msupplus{}].
\mforall{}[e:E]. \mforall{}[i:Id].
\muparrow{}e \mmember{}\msubb{} X supposing e is first@ i s.t. q.((\muparrow{}q \mmember{}\msubb{} X) \mwedge{} Q[q]) \mvee{} (||filter(\mlambda{}e.P[e];\mleq{}(X)(q))|| = n)
Date html generated:
2015_07_21-PM-03_41_50
Last ObjectModification:
2015_02_04-PM-06_13_06
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