Nuprl Lemma : bind-class-assoc
∀[Info,T,S,U:Type]. ∀[X:EClass(T)]. ∀[Y:T ⟶ EClass(S)]. ∀[Z:S ⟶ EClass(U)].
(X >x> Y[x] >y> Z[y] = X >x> Y[x] >y> Z[y] ∈ EClass(U))
Proof
Definitions occuring in Statement :
bind-class: X >x> Y[x],
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bind-class: X >x> Y[x],
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
squash: ↓T,
true: True,
top: Top,
guard: {T},
bag-filter: [x∈b|p[x]],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
cand: A c∧ B,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
decidable: Dec(P)
Latex:
\mforall{}[Info,T,S,U:Type]. \mforall{}[X:EClass(T)]. \mforall{}[Y:T {}\mrightarrow{} EClass(S)]. \mforall{}[Z:S {}\mrightarrow{} EClass(U)].
(X >x> Y[x] >y> Z[y] = X >x> Y[x] >y> Z[y])
Date html generated:
2016_05_16-PM-02_27_14
Last ObjectModification:
2016_01_17-PM-07_56_54
Theory : event-ordering
Home
Index