Nuprl Lemma : fpf-contains-union-join-right2
∀[A,V:Type]. ∀[B:A ─→ Type].
∀eq:EqDecider(A). ∀f,h,g:a:A fp-> B[a] List. ∀R:(V List) ─→ V ─→ 𝔹.
fpf-union-compatible(A;V;x.B[x];eq;R;f;g) ⇒ h ⊆⊆ g ⇒ h ⊆⊆ fpf-union-join(eq;R;f;g)
supposing fpf-single-valued(A;eq;x.B[x];V;g)
supposing ∀a:A. (B[a] ⊆r V)
Proof
Definitions occuring in Statement :
fpf-union-join: fpf-union-join(eq;R;f;g),
fpf-contains: f ⊆⊆ g,
fpf-single-valued: fpf-single-valued(A;eq;x.B[x];V;g),
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],
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
l_member_wf,
fpf-ap_wf,
list_wf,
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
fpf-contains_wf,
fpf-union-compatible_wf,
fpf-single-valued_wf,
bool_wf,
fpf_wf,
deq_wf,
all_wf,
subtype_rel_wf,
fpf-union-join-dom,
assert_elim,
subtype_base_sq,
bool_subtype_base,
fpf-union-contains2,
fpf-union-join-ap,
l_all_iff,
fpf-cap_wf,
nil_wf,
fpf-union_wf,
subtype_rel_dep_function,
subtype_rel_list,
subtype_rel_self,
select_wf,
sq_stable__le,
int_seg_wf,
length_wf,
equal-wf-T-base,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
\mforall{}[A,V:Type]. \mforall{}[B:A {}\mrightarrow{} Type].
\mforall{}eq:EqDecider(A). \mforall{}f,h,g:a:A fp-> B[a] List. \mforall{}R:(V List) {}\mrightarrow{} V {}\mrightarrow{} \mBbbB{}.
fpf-union-compatible(A;V;x.B[x];eq;R;f;g) {}\mRightarrow{} h \msubseteq{}\msubseteq{} g {}\mRightarrow{} h \msubseteq{}\msubseteq{} fpf-union-join(eq;R;f;g)
supposing fpf-single-valued(A;eq;x.B[x];V;g)
supposing \mforall{}a:A. (B[a] \msubseteq{}r V)
Date html generated:
2015_07_17-AM-11_07_49
Last ObjectModification:
2015_01_28-AM-07_48_24
Home
Index