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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
sv-class: Singlevalued(X),
all: ∀x:A. B[x],
map-class: (f[v] where v from X),
es-filter-image: f[X],
eclass-compose1: f o X,
eclass-val: X(e),
in-eclass: e ∈b X,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
bfalse: ff,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
rev_uimplies: rev_uimplies(P;Q)
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:
2016_05_17-AM-07_17_37
Last ObjectModification:
2015_12_29-AM-00_05_36
Theory : event-ordering
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