Nuprl Lemma : swap_swap
∀[T:Type]. ∀[L1:T List]. ∀[i,j:ℕ||L1||]. (swap(swap(L1;i;j);i;j) = L1 ∈ (T List))
Proof
Definitions occuring in Statement :
swap: swap(L;i;j),
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
guard: {T},
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
le: A ≤ B,
less_than: a < b,
nat: ℕ,
cand: A c∧ B,
subtype_rel: A ⊆r B,
ge: i ≥ j ,
true: True,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
swap_length,
swap_wf,
int_seg_properties,
decidable__lt,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
lelt_wf,
list_extensionality,
less_than_wf,
nat_wf,
int_seg_wf,
length_wf,
list_wf,
zero-le-nat,
nat_properties,
flip_wf,
length_wf_nat,
select_wf,
decidable__le,
intformle_wf,
itermConstant_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
equal_wf,
squash_wf,
le_wf,
flip_twice,
iff_weakening_equal,
true_wf,
swap_select
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
cumulativity,
hypothesis,
setElimination,
rename,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
lambdaFormation,
axiomEquality,
universeEquality,
applyEquality,
imageElimination,
productEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[L1:T List]. \mforall{}[i,j:\mBbbN{}||L1||]. (swap(swap(L1;i;j);i;j) = L1)
Date html generated:
2017_10_01-AM-08_38_02
Last ObjectModification:
2017_07_26-PM-04_26_52
Theory : list!
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