Nuprl Lemma : fpf-union-compatible-self
∀[A,C:Type]. ∀[B:A ─→ Type].
∀eq:EqDecider(A). ∀f:x:A fp-> B[x] List. ∀R:(C List) ─→ C ─→ 𝔹. fpf-union-compatible(A;C;x.B[x];eq;R;f;f)
supposing ∀a:A. (B[a] ⊆r C)
Proof
Definitions occuring in Statement :
fpf-union-compatible: fpf-union-compatible(A;C;x.B[x];eq;R;f;g),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
list: T List,
bool: 𝔹,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
select_wf,
fpf-ap_wf,
sq_stable__le,
select_member,
lelt_wf,
length_wf,
l_member_wf,
or_wf,
list_wf,
subtype_rel_list,
not_wf,
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
bool_wf,
fpf_wf,
deq_wf,
all_wf,
subtype_rel_wf
\mforall{}[A,C:Type]. \mforall{}[B:A {}\mrightarrow{} Type].
\mforall{}eq:EqDecider(A). \mforall{}f:x:A fp-> B[x] List. \mforall{}R:(C List) {}\mrightarrow{} C {}\mrightarrow{} \mBbbB{}.
fpf-union-compatible(A;C;x.B[x];eq;R;f;f)
supposing \mforall{}a:A. (B[a] \msubseteq{}r C)
Date html generated:
2015_07_17-AM-09_16_53
Last ObjectModification:
2015_01_28-AM-07_51_46
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