Nuprl Lemma : primed-class-opt_eq_class-opt-class-primed
∀[Info,T:Type]. ∀[init:Id ⟶ bag(T)]. ∀[X:EClass(T)]. (Prior(X)?init = Prior(X)?λl.init l| | ∈ EClass(T))
Proof
Definitions occuring in Statement :
class-opt-class: X?Y,
primed-class-opt: Prior(X)?b,
primed-class: Prior(X),
simple-loc-comb0: λl.b[l]| |,
eclass: EClass(A[eo; e]),
Id: Id,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
simple-loc-comb0: λl.b[l]| |,
primed-class: Prior(X),
class-opt-class: X?Y,
primed-class-opt: Prior(X)?b,
eclass: EClass(A[eo; e]),
select: L[n],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
simple-loc-comb: F|Loc; Xs|,
subtype_rel: A ⊆r B,
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]},
guard: {T},
iff: P ⇐⇒ Q,
lt_int: i <z j,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
not: ¬A,
true: True,
bool: 𝔹,
unit: Unit,
btrue: tt,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
squash: ↓T
Latex:
\mforall{}[Info,T:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(T)]. \mforall{}[X:EClass(T)]. (Prior(X)?init = Prior(X)?\mlambda{}l.init l| |)
Date html generated:
2016_05_16-PM-11_49_24
Last ObjectModification:
2016_01_17-PM-07_01_42
Theory : event-ordering
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