Nuprl Lemma : map-class_functionality
∀[Info,T,A,B:Type]. ∀[f:A ─→ T]. ∀[g:B ─→ T]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
(f[a] where a from X) = (g[b] where b from Y) ∈ EClass(T)
supposing ∀es:EO+(Info). ∀e:E. ((↑e ∈b X ⇐⇒ ↑e ∈b Y) ∧ ((↑e ∈b X) ⇒ (↑e ∈b Y) ⇒ (f[X(e)] = g[Y(e)] ∈ T)))
Proof
Definitions occuring in Statement :
map-class: (f[v] where v from X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
es-interface-extensionality,
map-class_wf,
is-map-class,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
es-E-interface-property,
assert_wf,
in-eclass_wf,
top_wf,
all_wf,
event-ordering+_wf,
iff_wf,
eclass-val_wf,
eclass_wf,
map-class-val,
bool_wf,
eqtt_to_assert,
bag_size_single_lemma,
false_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
bag_size_empty_lemma
\mforall{}[Info,T,A,B:Type]. \mforall{}[f:A {}\mrightarrow{} T]. \mforall{}[g:B {}\mrightarrow{} T]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)].
(f[a] where a from X) = (g[b] where b from Y)
supposing \mforall{}es:EO+(Info). \mforall{}e:E.
((\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \muparrow{}e \mmember{}\msubb{} Y) \mwedge{} ((\muparrow{}e \mmember{}\msubb{} X) {}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} Y) {}\mRightarrow{} (f[X(e)] = g[Y(e)])))
Date html generated:
2015_07_17-PM-01_08_37
Last ObjectModification:
2015_01_27-PM-10_36_33
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