Nuprl Lemma : es-interface-map-val
∀[Info,A:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(A)]. ∀[f:A ⟶ E(X) ⟶ bag(Top)]. ∀[e:E].
es-interface-map(f;X)(e) ~ only(f X(e) e) supposing ↑e ∈b es-interface-map(f;X)
Proof
Definitions occuring in Statement :
es-interface-map: es-interface-map(f;X),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t,
bag-only: only(bs),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
eclass-val: X(e),
es-interface-map: es-interface-map(f;X),
in-eclass: e ∈b X,
let: let,
member: t ∈ T,
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
exposed-it: exposed-it,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
nat: ℕ,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
eq_int: (i =z j),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
cand: A c∧ B,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
rev_uimplies: rev_uimplies(P;Q),
es-E-interface: E(X)
Latex:
\mforall{}[Info,A:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(A)]. \mforall{}[f:A {}\mrightarrow{} E(X) {}\mrightarrow{} bag(Top)]. \mforall{}[e:E].
es-interface-map(f;X)(e) \msim{} only(f X(e) e) supposing \muparrow{}e \mmember{}\msubb{} es-interface-map(f;X)
Date html generated:
2016_05_16-PM-10_33_30
Last ObjectModification:
2016_01_17-PM-07_23_28
Theory : event-ordering
Home
Index