Nuprl Lemma : es-fix-sqequal
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:E(X) ⟶ E(X)]. ∀[e:E(X)]. f**(e) ~ e supposing (f e) = e ∈ E
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-fix: f**(e),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
es-E-interface: E(X),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
prop: ℙ,
es-fix: f**(e),
fix: f**(x),
ycomb: Y,
not: ¬A,
implies: P ⇒ Q,
false: False,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:E(X) {}\mrightarrow{} E(X)]. \mforall{}[e:E(X)].
f**(e) \msim{} e supposing (f e) = e
Date html generated:
2016_05_16-PM-10_18_42
Last ObjectModification:
2015_12_29-AM-11_16_01
Theory : event-ordering
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