Nuprl Lemma : fpf-cap_functionality
∀[A:Type]. ∀[d1,d2:EqDecider(A)]. ∀[B:A ─→ Type]. ∀[f:a:A fp-> B[a]]. ∀[x:A]. ∀[z:B[x]]. (f(x)?z = 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],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
bool_wf,
fpf-ap_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
fpf_ap_pair_lemma,
assert-deq-member,
l_member_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
fpf_wf,
deq_wf
\mforall{}[A:Type]. \mforall{}[d1,d2:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[x:A]. \mforall{}[z:B[x]].
(f(x)?z = f(x)?z)
Date html generated:
2015_07_17-AM-09_17_59
Last ObjectModification:
2015_01_28-AM-07_50_22
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