Nuprl Lemma : fpf-cap_wf
∀[A:Type]. ∀[B:A ─→ Type]. ∀[f:a:A fp-> B[a]]. ∀[eq:EqDecider(A)]. ∀[x:A]. ∀[z:B[x]]. (f(x)?z ∈ B[x])
Proof
Definitions occuring in Statement :
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ─→ B[x],
universe: Type
Lemmas :
deq_wf,
fpf_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
bool_wf,
fpf-ap_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[eq:EqDecider(A)]. \mforall{}[x:A]. \mforall{}[z:B[x]].
(f(x)?z \mmember{} B[x])
Date html generated:
2015_07_17-AM-09_16_29
Last ObjectModification:
2015_01_28-AM-07_52_03
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