Nuprl Lemma : fpf-join-list-ap
∀[A:Type]
∀eq:EqDecider(A)
∀[B:A ─→ Type]
∀L:a:A fp-> B[a] List. ∀x:A. (∃f∈L. (↑x ∈ dom(f)) ∧ (⊕(L)(x) = f(x) ∈ B[x])) supposing ↑x ∈ dom(⊕(L))
Proof
Definitions occuring in Statement :
fpf-join-list: ⊕(L),
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
l_exists: (∃x∈L. P[x]),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
fpf-join-dom,
fpf-join_wf,
subtype_top,
top_wf,
subtype-fpf2,
fpf-dom_wf,
assert_wf,
l_member_wf,
fpf_wf,
l_exists_wf,
iff_weakening_equal,
fpf-ap_wf,
fpf-join-list_wf,
fpf-join-ap-left,
sq_stable__le,
select_wf,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
eqtt_to_assert,
bool_wf,
fpf-join-ap
\mforall{}[A:Type]
\mforall{}eq:EqDecider(A)
\mforall{}[B:A {}\mrightarrow{} Type]
\mforall{}L:a:A fp-> B[a] List. \mforall{}x:A.
(\mexists{}f\mmember{}L. (\muparrow{}x \mmember{} dom(f)) \mwedge{} (\moplus{}(L)(x) = f(x))) supposing \muparrow{}x \mmember{} dom(\moplus{}(L))
Date html generated:
2015_07_17-AM-09_21_01
Last ObjectModification:
2015_07_16-AM-09_51_32
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