Nuprl Lemma : permutation-sv-list
∀[A:Type]. ∀[L1,L2:A List]. (single-valued-list(L1;A) ⇒ permutation(A;L1;L2) ⇒ (L1 = L2 ∈ (A List)))
Proof
Definitions occuring in Statement :
single-valued-list: single-valued-list(L;T),
permutation: permutation(T;L1;L2),
list: T List,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
uimplies: b supposing a,
nat: ℕ,
permutation: permutation(T;L1;L2),
exists: ∃x:A. B[x],
and: P ∧ Q,
top: Top,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
cand: A c∧ B,
single-valued-list: single-valued-list(L;T),
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[A:Type]. \mforall{}[L1,L2:A List]. (single-valued-list(L1;A) {}\mRightarrow{} permutation(A;L1;L2) {}\mRightarrow{} (L1 = L2))
Date html generated:
2016_05_17-AM-11_10_21
Last ObjectModification:
2016_01_18-AM-00_10_34
Theory : process-model
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