Nuprl Lemma : fpf-restrict_wf
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[f:x:A fp-> B[x]]. ∀[P:A ⟶ 𝔹]. (fpf-restrict(f;P) ∈ x:{x:A| ↑(P x)} fp-> B[x])
Proof
Definitions occuring in Statement :
fpf-restrict: fpf-restrict(f;P),
fpf: a:A fp-> B[a],
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fpf: a:A fp-> B[a],
fpf-restrict: fpf-restrict(f;P),
pi2: snd(t),
fpf-domain: fpf-domain(f),
mk_fpf: mk_fpf(L;f),
pi1: fst(t),
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
uimplies: b supposing a,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
cand: A c∧ B,
guard: {T},
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
iff: P ⇐⇒ Q
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:x:A fp-> B[x]]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. (fpf-restrict(f;P) \mmember{} x:\{x:A| \muparrow{}(P x)\} f\000Cp-> B[x])
Date html generated:
2016_05_16-AM-11_33_12
Last ObjectModification:
2016_01_17-PM-03_49_15
Theory : event-ordering
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