Nuprl Lemma : fpf-join-empty-sq
∀[A:Type]. ∀[B:A ─→ Type]. ∀[f:a:A fp-> B[a]]. ∀[eq:EqDecider(A)]. (⊗ ⊕ f ~ <fst(f), λa.((snd(f)) a)>)
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-empty: ⊗,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
pi2: snd(t),
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
pair: <a, b>,
universe: Type,
sqequal: s ~ t
Lemmas :
fpf_ap_pair_lemma,
list_ind_nil_lemma,
deq_member_nil_lemma,
filter_tt,
subtype_rel_list,
top_wf,
deq_wf,
fpf_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[eq:EqDecider(A)].
(\motimes{} \moplus{} f \msim{} <fst(f), \mlambda{}a.((snd(f)) a)>)
Date html generated:
2015_07_17-AM-09_19_10
Last ObjectModification:
2015_01_28-AM-07_48_58
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