Nuprl Lemma : fpf-union-contains
∀[A:Type]. ∀[B:A ─→ Type].
∀eq:EqDecider(A). ∀f,g:x:A fp-> B[x] List. ∀x:A. ∀R:∩a:A. ((B[a] List) ─→ B[a] ─→ 𝔹). f(x)?[] ⊆ fpf-union(f;g;eq;R;x)
Proof
Definitions occuring in Statement :
fpf-union: fpf-union(f;g;eq;R;x),
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
l_contains: A ⊆ B,
nil: [],
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
isect: ∩x:A. B[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
list_wf,
bool_wf,
eqtt_to_assert,
l_contains_append,
fpf-ap_wf,
filter_wf5,
subtype_rel_dep_function,
l_member_wf,
subtype_rel_self,
set_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
l_contains_weakening,
l_contains_nil,
nil_wf,
fpf_wf,
deq_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type].
\mforall{}eq:EqDecider(A). \mforall{}f,g:x:A fp-> B[x] List. \mforall{}x:A. \mforall{}R:\mcap{}a:A. ((B[a] List) {}\mrightarrow{} B[a] {}\mrightarrow{} \mBbbB{}).
f(x)?[] \msubseteq{} fpf-union(f;g;eq;R;x)
Date html generated:
2015_07_17-AM-09_16_43
Last ObjectModification:
2015_01_28-AM-07_51_51
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