Nuprl Lemma : fpf-union-compatible_wf
∀[A,C:Type]. ∀[B:A ⟶ Type].
∀[eq:EqDecider(A)]. ∀[f,g:x:A fp-> B[x] List]. ∀[R:(C List) ⟶ C ⟶ 𝔹].
(fpf-union-compatible(A;C;x.B[x];eq;R;f;g) ∈ ℙ)
supposing ∀x:A. (B[x] ⊆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],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
fpf-union-compatible: fpf-union-compatible(A;C;x.B[x];eq;R;f;g),
so_apply: x[s],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
or: P ∨ Q,
exists: ∃x:A. B[x]
Latex:
\mforall{}[A,C:Type]. \mforall{}[B:A {}\mrightarrow{} Type].
\mforall{}[eq:EqDecider(A)]. \mforall{}[f,g: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;g) \mmember{} \mBbbP{})
supposing \mforall{}x:A. (B[x] \msubseteq{}r C)
Date html generated:
2016_05_16-AM-11_05_29
Last ObjectModification:
2015_12_29-AM-09_13_55
Theory : event-ordering
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