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
Lemmas :
ap_fpf_restrict_lemma,
top_wf,
deq_wf,
fpf_wf,
assert_wf,
bool_wf,
subtype_base_sq,
bool_subtype_base,
iff_imp_equal_bool,
domain_fpf_restrict_lemma,
member-fpf-domain,
l_member_wf,
fpf-domain_wf,
member_filter,
filter_wf5,
subtype_rel_dep_function,
subtype_rel_self,
set_wf,
iff_wf
\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:
2015_07_17-AM-11_15_02
Last ObjectModification:
2015_01_28-AM-07_39_07
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