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],
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],
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-union-compatible: fpf-union-compatible(A;C;x.B[x];eq;R;f;g),
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
cand: A c∧ B,
so_apply: x[s],
so_lambda: λ2x.t[x],
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B
Latex:
\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:
2016_05_16-AM-11_05_45
Last ObjectModification:
2016_01_17-PM-03_47_41
Theory : event-ordering
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