Nuprl Lemma : interleaving_symmetry
∀[T:Type]. ∀L,L1,L2:T List. (interleaving(T;L1;L2;L) ⇐⇒ interleaving(T;L2;L1;L))
Proof
Definitions occuring in Statement :
interleaving: interleaving(T;L1;L2;L),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
interleaving: interleaving(T;L1;L2;L),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
nat: ℕ,
guard: {T},
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
false: False,
uiff: uiff(P;Q),
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
prop: ℙ,
disjoint_sublists: disjoint_sublists(T;L1;L2;L),
cand: A c∧ B,
int_seg: {i..j-},
lelt: i ≤ j < k,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
less_than: a < b,
squash: ↓T,
le: A ≤ B,
so_apply: x[s],
rev_implies: P ⇐ Q
Lemmas referenced :
nat_properties,
decidable__equal_int,
length_wf,
add-is-int-iff,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_wf,
false_wf,
non_neg_length,
decidable__le,
intformle_wf,
itermConstant_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
le_wf,
int_seg_properties,
equal_wf,
int_seg_wf,
increasing_wf,
length_wf_nat,
all_wf,
select_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
lelt_wf,
not_wf,
exists_wf,
nat_wf,
add_nat_wf,
disjoint_sublists_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
introduction,
extract_by_obid,
isectElimination,
equalityTransitivity,
hypothesis,
equalitySymmetry,
applyLambdaEquality,
setElimination,
rename,
hypothesisEquality,
dependent_functionElimination,
addEquality,
cumulativity,
unionElimination,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
baseClosed,
independent_isectElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
dependent_set_memberEquality,
because_Cache,
applyEquality,
functionExtensionality,
independent_functionElimination,
productEquality,
imageElimination,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L,L1,L2:T List. (interleaving(T;L1;L2;L) \mLeftarrow{}{}\mRightarrow{} interleaving(T;L2;L1;L))
Date html generated:
2017_10_01-AM-08_36_15
Last ObjectModification:
2017_07_26-PM-04_26_10
Theory : list!
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