Nuprl Lemma : pi-add_wf
∀[A:Type]. ∀[B:A ─→ Type]. ∀[eq:EqDecider(A)]. ∀[q:(a:A × B[a]) List]. ∀[st:a:A fp-> B[a]].
(pi-add(eq;q;st) ∈ a:A fp-> B[a])
Proof
Definitions occuring in Statement :
pi-add: pi-add(eq;q;st),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
list: T List,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type
Lemmas :
list_accum_wf,
fpf-join_wf,
fpf-single_wf,
fpf_wf,
list_wf,
deq_wf
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[q:(a:A \mtimes{} B[a]) List]. \mforall{}[st:a:A fp-> B[a]].
(pi-add(eq;q;st) \mmember{} a:A fp-> B[a])
Date html generated:
2015_07_23-AM-11_58_04
Last ObjectModification:
2015_01_29-AM-07_40_06
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