Nuprl Lemma : fpf-join-assoc
∀[A:Type]. ∀[B:A ─→ Type]. ∀[eq:EqDecider(A)]. ∀[f,g,h:a:A fp-> B[a]]. (f ⊕ g ⊕ h = f ⊕ g ⊕ h ∈ a:A fp-> B[a])
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
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 :
set_wf,
l_member_wf,
list_wf,
deq_wf,
append_assoc,
append_wf,
squash_wf,
true_wf,
filter_append,
bnot_wf,
deq-member_wf,
filter_wf5,
filter_filter,
bool_wf,
eqtt_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
eqff_to_assert,
assert-bnot,
assert-deq-member,
member_filter,
assert_wf,
or_wf,
not_wf,
iff_wf,
member_append,
iff_imp_equal_bool,
iff_transitivity,
iff_weakening_uiff,
assert_of_band,
assert_of_bnot,
equal-wf-T-base
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g,h:a:A fp-> B[a]]. (f \moplus{} g \moplus{} h = f \moplus{} g \moplus{} h)
Date html generated:
2015_07_17-AM-09_19_37
Last ObjectModification:
2015_01_28-AM-07_58_08
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