Nuprl Lemma : sv-bag-is-bag-rep-lousy-proof
∀[A:Type]. ∀[as:bag(A)]. ∀a:A. (a ↓∈ as ⇒ (as = bag-rep(#(as);a) ∈ bag(A))) supposing single-valued-bag(as;A)
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T,
single-valued-bag: single-valued-bag(b;T),
bag-member: x ↓∈ bs,
bag-rep: bag-rep(n;x),
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
top: Top,
nat: ℕ,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
exists: ∃x:A. B[x],
squash: ↓T,
single-valued-list: single-valued-list(L;T),
bag-size: #(bs),
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
true: True
Latex:
\mforall{}[A:Type]. \mforall{}[as:bag(A)].
\mforall{}a:A. (a \mdownarrow{}\mmember{} as {}\mRightarrow{} (as = bag-rep(\#(as);a))) supposing single-valued-bag(as;A)
Date html generated:
2016_05_17-AM-11_11_45
Last ObjectModification:
2016_01_18-AM-00_09_59
Theory : process-model
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