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],
list: T List,
deq: EqDecider(T),
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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
fpf-single-valued: fpf-single-valued(A;eq;x.B[x];V;g),
implies: P ⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
top: Top,
fpf-contains: f ⊆⊆ g,
cand: A c∧ B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
or: P ∨ Q,
true: True,
l_contains: A ⊆ B,
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
less_than: a < b,
squash: ↓T,
fpf-cap: f(x)?z,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff
Latex:
\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:
2016_05_16-AM-11_15_01
Last ObjectModification:
2016_01_17-PM-03_48_15
Theory : event-ordering
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