Nuprl Lemma : fpf-restrict-cap
∀[A:Type]. ∀[P:A ⟶ 𝔹]. ∀[x:A].
∀[f:x:A fp-> Top]. ∀[eq:EqDecider(A)]. ∀[z:Top]. (fpf-restrict(f;P)(x)?z ~ f(x)?z) supposing ↑(P x)
Proof
Definitions occuring in Statement :
fpf-restrict: fpf-restrict(f;P),
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
fpf-cap: f(x)?z,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
guard: {T},
subtype_rel: A ⊆r B
Latex:
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[x:A].
\mforall{}[f:x:A fp-> Top]. \mforall{}[eq:EqDecider(A)]. \mforall{}[z:Top]. (fpf-restrict(f;P)(x)?z \msim{} f(x)?z)
supposing \muparrow{}(P x)
Date html generated:
2016_05_16-AM-11_33_59
Last ObjectModification:
2015_12_29-AM-09_29_30
Theory : event-ordering
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