Nuprl Lemma : es-E-mk-extended-eo
∀[Info,E:Type]. ∀[dom:E ⟶ 𝔹]. ∀[l:E ⟶ Id]. ∀[R:E ⟶ E ⟶ ℙ]. ∀[locless:E ⟶ E ⟶ 𝔹]. ∀[pred:E ⟶ E]. ∀[rank:E ⟶ ℕ].
∀[info:E ⟶ Info].
∀x:E. ((x ∈ E) ∧ (↑(dom x)))
Proof
Definitions occuring in Statement :
mk-extended-eo: mk-extended-eo,
es-E: E,
Id: Id,
nat: ℕ,
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
true: True,
assert: ↑b,
guard: {T},
implies: P ⇒ Q,
sq_type: SQType(T),
uimplies: b supposing a,
cand: A c∧ B,
and: P ∧ Q,
btrue: tt,
mk-eo-record: mk-eo-record(E;dom;l;R;locless;pred;rank),
mk-eo: mk-eo(E;dom;l;R;locless;pred;rank),
bfalse: ff,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
top: Top,
member: t ∈ T,
all: ∀x:A. B[x],
es-E: E,
mk-extended-eo: mk-extended-eo,
uall: ∀[x:A]. B[x]
Latex:
\mforall{}[Info,E:Type]. \mforall{}[dom:E {}\mrightarrow{} \mBbbB{}]. \mforall{}[l:E {}\mrightarrow{} Id]. \mforall{}[R:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \mforall{}[locless:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbB{}].
\mforall{}[pred:E {}\mrightarrow{} E]. \mforall{}[rank:E {}\mrightarrow{} \mBbbN{}]. \mforall{}[info:E {}\mrightarrow{} Info].
\mforall{}x:E. ((x \mmember{} E) \mwedge{} (\muparrow{}(dom x)))
Date html generated:
2016_05_17-AM-08_19_09
Last ObjectModification:
2015_12_28-PM-11_06_20
Theory : event-ordering
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