Nuprl Lemma : State-comb-exists
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E].
↓∃v:B. v ∈ State-comb(init;f;X)(e) supposing #(init loc(e)) > 0
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
gt: i > j,
exists: ∃x:A. B[x],
squash: ↓T,
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Lemmas :
nat_wf,
bag-size_wf,
event-ordering+_subtype,
es-loc_wf,
bag-member-iff-size,
assert_of_bnot,
eqff_to_assert,
iff_weakening_uiff,
iff_transitivity,
assert-bag-null,
eqtt_to_assert,
uiff_transitivity,
not_wf,
bnot_wf,
bag_wf,
assert_wf,
equal-wf-T-base,
bool_wf,
bag-null_wf,
State-comb_wf,
classrel_wf,
rec-combined-class-opt-1-classrel,
squash_wf,
es-p-local-pred_wf,
exists_wf,
es-E_wf,
es-locl_wf,
btrue_neq_bfalse,
assert_elim,
es-locl-first,
primed-class-opt-classrel,
le_weakening,
empty-bag-iff-size,
bag-member-empty-iff,
bag-member_wf,
event-ordering+_wf,
eclass_wf,
primed-class-opt_wf,
bag-member-lifting-2,
iff_weakening_equal,
es-pred-loc-base,
true_wf,
gt_wf,
es-causl_weakening,
es-pred-locl,
es-pred_wf,
all_wf,
es-causl_irreflexivity,
es-causle_weakening,
es-causl_transitivity2,
es-locl_irreflexivity,
es-le_weakening_eq,
es-locl_transitivity2,
es-pred_property
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mdownarrow{}\mexists{}v:B. v \mmember{} State-comb(init;f;X)(e) supposing \#(init loc(e)) > 0
Date html generated:
2015_07_22-PM-00_20_52
Last ObjectModification:
2015_07_16-AM-09_39_32
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