Nuprl Lemma : map-pair-prior
∀[Info,A,B,C,D:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[f:(A × B) ─→ C]. ∀[g:(A × D) ─→ C]. ∀[h:B ─→ D].
(f[p] where p from X;Y) = (g[p] where p from X;(h[y] where y from Y)) ∈ EClass(C)
supposing ∀a:A. ∀b:B. (f[<a, b>] = g[<a, h[b]>] ∈ C)
Proof
Definitions occuring in Statement :
es-interface-pair-prior: X;Y,
map-class: (f[v] where v from X),
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ─→ B[x],
pair: <a, b>,
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
es-interface-extensionality,
map-class_wf,
es-interface-pair-prior_wf,
in-eclass_wf,
bool_wf,
eqtt_to_assert,
bag_size_single_lemma,
false_wf,
eqff_to_assert,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
subtype_top,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
bag_size_empty_lemma,
assert_wf,
all_wf,
eclass_wf,
event-ordering+_wf,
is-map-class,
eclass-val_wf,
es-prior-val_wf,
iff_weakening_equal,
is-pair-prior,
map-class-val,
pair-prior-val
Latex:
\mforall{}[Info,A,B,C,D:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[f:(A \mtimes{} B) {}\mrightarrow{} C]. \mforall{}[g:(A \mtimes{} D) {}\mrightarrow{} C].
\mforall{}[h:B {}\mrightarrow{} D].
(f[p] where p from X;Y) = (g[p] where p from X;(h[y] where y from Y))
supposing \mforall{}a:A. \mforall{}b:B. (f[<a, b>] = g[<a, h[b]>])
Date html generated:
2015_07_21-PM-03_47_52
Last ObjectModification:
2015_02_04-PM-06_11_15
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