Nuprl Lemma : fpf-empty-join
∀[A:Type]. ∀[B:A ─→ Type]. ∀[f:a:A fp-> B[a]]. ∀[eq:EqDecider(A)]. (f ⊕ ⊗ = f ∈ a:A fp-> B[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],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
fpf_ap_pair_lemma,
filter_nil_lemma,
append_back_nil,
append-nil,
subtype_rel_list,
top_wf,
set_wf,
l_member_wf,
deq_wf,
fpf_wf,
deq-member_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
iff_transitivity,
iff_weakening_uiff,
eqtt_to_assert,
assert-deq-member,
eqff_to_assert,
assert_of_bnot
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[eq:EqDecider(A)]. (f \moplus{} \motimes{} = f)
Date html generated:
2015_07_17-AM-09_19_07
Last ObjectModification:
2015_01_28-AM-07_50_32
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