Nuprl Lemma : fpf-join-list-ap
∀[A:Type]
∀eq:EqDecider(A)
∀[B:A ⟶ Type]
∀L:a:A fp-> B[a] List. ∀x:A. (∃f∈L. (↑x ∈ dom(f)) ∧ (⊕(L)(x) = f(x) ∈ B[x])) supposing ↑x ∈ dom(⊕(L))
Proof
Definitions occuring in Statement :
fpf-join-list: ⊕(L),
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
l_exists: (∃x∈L. P[x]),
list: T List,
deq: EqDecider(T),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
and: P ∧ Q,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
top: Top,
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
fpf-join-list: ⊕(L),
fpf-empty: ⊗,
fpf-dom: x ∈ dom(f),
pi1: fst(t),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
false: False,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
cand: A c∧ B,
guard: {T},
not: ¬A,
l_exists: (∃x∈L. P[x]),
exists: ∃x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
less_than: a < b,
squash: ↓T,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
bnot: ¬bb
Latex:
\mforall{}[A:Type]
\mforall{}eq:EqDecider(A)
\mforall{}[B:A {}\mrightarrow{} Type]
\mforall{}L:a:A fp-> B[a] List. \mforall{}x:A.
(\mexists{}f\mmember{}L. (\muparrow{}x \mmember{} dom(f)) \mwedge{} (\moplus{}(L)(x) = f(x))) supposing \muparrow{}x \mmember{} dom(\moplus{}(L))
Date html generated:
2016_05_16-AM-11_12_56
Last ObjectModification:
2016_01_17-PM-03_48_30
Theory : event-ordering
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