Nuprl Lemma : sub-es-pred_wf
∀[es:EO]. ∀[dom:E ⟶ 𝔹]. ∀[e:E]. (sub-es-pred(es;dom;e) ∈ {e:E| ↑(dom e)} ?)
Proof
Definitions occuring in Statement :
sub-es-pred: sub-es-pred(es;dom;e),
es-E: E,
event_ordering: EO,
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
union: left + right
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
sub-es-pred: sub-es-pred(es;dom;e),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
exposed-bfalse: exposed-bfalse
Latex:
\mforall{}[es:EO]. \mforall{}[dom:E {}\mrightarrow{} \mBbbB{}]. \mforall{}[e:E]. (sub-es-pred(es;dom;e) \mmember{} \{e:E| \muparrow{}(dom e)\} ?)
Date html generated:
2016_05_16-AM-10_25_46
Last ObjectModification:
2016_01_17-PM-01_22_34
Theory : new!event-ordering
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