Nuprl Lemma : primed-class-opt_eq_class-opt-primed
∀[Info,T:Type]. ∀[b:Id ⟶ bag(T)]. ∀[X:EClass(T)]. (Prior(X)?b = Prior(X)?b ∈ EClass(T))
Proof
Definitions occuring in Statement :
class-opt: X?b,
primed-class-opt: Prior(X)?b,
primed-class: Prior(X),
eclass: EClass(A[eo; e]),
Id: Id,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
primed-class: Prior(X),
class-opt: X?b,
primed-class-opt: Prior(X)?b,
eclass: EClass(A[eo; e]),
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
nat: ℕ,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
so_apply: x[s],
or: P ∨ Q,
sq_exists: ∃x:{A| B[x]},
uimplies: b supposing a,
not: ¬A,
false: False,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
guard: {T},
lt_int: i <z j,
assert: ↑b,
true: True,
squash: ↓T
Latex:
\mforall{}[Info,T:Type]. \mforall{}[b:Id {}\mrightarrow{} bag(T)]. \mforall{}[X:EClass(T)]. (Prior(X)?b = Prior(X)?b)
Date html generated:
2016_05_16-PM-11_49_06
Last ObjectModification:
2016_01_17-PM-07_04_08
Theory : event-ordering
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