Nuprl Lemma : fpf-sub-set
∀[A:Type]. ∀[P:A ─→ ℙ]. ∀[B:A ─→ Type]. ∀[eq:EqDecider(A)]. ∀[f,g:a:{a:A| P[a]} fp-> B[a]]. f ⊆ g supposing f ⊆ g
Proof
Definitions occuring in Statement :
fpf-sub: f ⊆ g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
universe: Type
Lemmas :
assert-deq-member,
subtype_rel_list,
select_wf,
sq_stable__le,
decidable__lt,
length_wf,
false_wf,
less-iff-le,
add_functionality_wrt_le,
add-swap,
add-commutes,
le-add-cancel,
set_wf,
and_wf,
equal_wf,
assert_wf,
deq-member_wf
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:a:\{a:A| P[a]\} fp-> B[a]].
f \msubseteq{} g supposing f \msubseteq{} g
Date html generated:
2015_07_17-AM-09_17_12
Last ObjectModification:
2015_01_28-AM-07_51_39
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