Nuprl Lemma : es-pred-wf-base
∀[es:EO]. ∀[e:es-base-E(es)]. (pred(e) ∈ es-base-E(es))
Proof
Definitions occuring in Statement :
es-pred: pred(e),
es-base-E: es-base-E(es),
event_ordering: EO,
uall: ∀[x:A]. B[x],
member: t ∈ T
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,
es-pred: pred(e),
let: let,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b
Latex:
\mforall{}[es:EO]. \mforall{}[e:es-base-E(es)]. (pred(e) \mmember{} es-base-E(es))
Date html generated:
2016_05_16-AM-09_16_02
Last ObjectModification:
2016_01_17-PM-01_31_23
Theory : new!event-ordering
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