Nuprl Lemma : fpf-as-apply-alist
∀[A,B:Type]. ∀[f:a:A fp-> B]. ∀[eq:EqDecider(A)].
(f = <fpf-domain(f), λx.outl(apply-alist(eq;map(λx.<x, f(x)>;fpf-domain(f));x))> ∈ a:A fp-> B)
Proof
Definitions occuring in Statement :
fpf-ap: f(x),
fpf-domain: fpf-domain(f),
fpf: a:A fp-> B[a],
apply-alist: apply-alist(eq;L;x),
map: map(f;as),
deq: EqDecider(T),
outl: outl(x),
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
pair: <a, b>,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fpf: a:A fp-> B[a],
fpf-domain: fpf-domain(f),
fpf-ap: f(x),
pi1: fst(t),
pi2: snd(t),
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than: a < b,
outl: outl(x),
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
squash: ↓T
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:a:A fp-> B]. \mforall{}[eq:EqDecider(A)].
(f = <fpf-domain(f), \mlambda{}x.outl(apply-alist(eq;map(\mlambda{}x.<x, f(x)>fpf-domain(f));x))>)
Date html generated:
2016_05_16-AM-11_05_08
Last ObjectModification:
2016_01_17-PM-03_48_04
Theory : event-ordering
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