Nuprl Lemma : bind-return-left
∀[Info,T,S:Type]. ∀[x:T]. ∀f:T ⟶ EClass(S). (return-class(x) >z> f[z] = f[x] ∈ EClass(S))
Proof
Definitions occuring in Statement :
return-class: return-class(x),
bind-class: X >x> Y[x],
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
eclass: EClass(A[eo; e]),
bind-class: X >x> Y[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
cand: A c∧ B,
or: P ∨ Q,
not: ¬A,
false: False,
cons: [a / b],
top: Top,
ge: i ≥ j ,
decidable: Dec(P),
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
squash: ↓T,
sq_stable: SqStable(P),
bag-append: as + bs,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
less_than': less_than'(a;b),
length: ||as||,
list_ind: list_ind,
nil: [],
it: ⋅,
single-bag: {x},
return-class: return-class(x),
uiff: uiff(P;Q),
bfalse: ff
Latex:
\mforall{}[Info,T,S:Type]. \mforall{}[x:T]. \mforall{}f:T {}\mrightarrow{} EClass(S). (return-class(x) >z> f[z] = f[x])
Date html generated:
2016_05_16-PM-02_26_21
Last ObjectModification:
2016_01_17-PM-07_51_31
Theory : event-ordering
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