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],
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pi-add: pi-add(eq;q;st),
so_apply: x[s],
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
pi1: fst(t),
pi2: snd(t),
so_apply: x[s1;s2]
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:
2016_05_17-AM-11_32_06
Last ObjectModification:
2015_12_29-PM-06_49_31
Theory : event-logic-applications
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