Nuprl Lemma : prior-or-latest
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
((X |- Y))' = ((X)' | (Y)') ∈ EClass(one_or_both(A;B)) supposing Singlevalued(X) ∧ Singlevalued(Y)
Proof
Definitions occuring in Statement :
es-or-latest: (X |- Y),
es-prior-val: (X)',
es-interface-or: (X | Y),
sv-class: Singlevalued(X),
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T,
one_or_both: one_or_both(A;B)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
or: P ∨ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
rev_implies: P ⇐ Q,
cand: A c∧ B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
sv-class: Singlevalued(X),
es-interface-or: (X | Y),
eclass-compose2: eclass-compose2(f;X;Y),
oob-apply: oob-apply(xs;ys),
eclass-val: X(e),
in-eclass: e ∈b X,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
es-prior-val: (X)',
eclass: EClass(A[eo; e]),
nat: ℕ,
squash: ↓T,
true: True,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla)
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)].
((X |\msupminus{} Y))' = ((X)' | (Y)') supposing Singlevalued(X) \mwedge{} Singlevalued(Y)
Date html generated:
2016_05_17-AM-08_14_19
Last ObjectModification:
2016_01_17-PM-02_51_53
Theory : event-ordering
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