Nuprl Lemma : es-interface-left-as-image
∀[Info,A,B:Type]. ∀[X:EClass(A + B)]. (left(X) = λx.case x of inl(a) => {a} | inr(b) => {}[X] ∈ EClass(A))
Proof
Definitions occuring in Statement :
es-interface-left: left(X),
es-filter-image: f[X],
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
union: left + right,
universe: Type,
equal: s = t ∈ T,
single-bag: {x},
empty-bag: {}
Lemmas :
in-eclass_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
subtype_top,
bool_wf,
eqtt_to_assert,
single-eclass-val,
eclass-val_wf,
equal_wf,
bag_wf,
bag-separate_wf,
single-bag_wf,
empty-bag_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
eclass_wf,
event-ordering+_wf,
filter_cons_lemma,
filter_nil_lemma,
map_cons_lemma,
map_nil_lemma
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A + B)]. (left(X) = \mlambda{}x.case x of inl(a) => \{a\} | inr(b) => \{\}[X])
Date html generated:
2015_07_21-PM-03_30_02
Last ObjectModification:
2015_01_27-PM-06_37_40
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