Nuprl Lemma : nil_interleaving
∀[T:Type]. ∀L1,L:T List. (interleaving(T;[];L1;L) ⇐⇒ L = L1 ∈ (T List))
Proof
Definitions occuring in Statement :
interleaving: interleaving(T;L1;L2;L),
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
uiff: uiff(P;Q),
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
guard: {T},
not: ¬A,
false: False,
less_than': less_than'(a;b),
le: A ≤ B,
nat: ℕ,
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
interleaving: interleaving(T;L1;L2;L),
disjoint_sublists: disjoint_sublists(T;L1;L2;L),
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
int_seg: {i..j-},
lelt: i ≤ j < k,
cand: A c∧ B,
less_than: a < b,
squash: ↓T
Lemmas referenced :
decidable__equal_int,
list_wf,
and_wf,
non_neg_length,
nil_wf,
disjoint_sublists_wf,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
add-is-int-iff,
decidable__le,
nat_properties,
le_wf,
false_wf,
add_nat_wf,
length_wf,
length_wf_nat,
nat_wf,
equal_wf,
length_of_nil_lemma,
disjoint_sublists_sublist,
proper_sublist_length,
stuck-spread,
istype-base,
int_seg_properties,
full-omega-unsat,
istype-int,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
istype-le,
istype-less_than,
int_seg_wf,
id_increasing,
istype-void,
select_wf,
increasing_wf
Rules used in proof :
universeEquality,
hyp_replacement,
applyEquality,
because_Cache,
independent_functionElimination,
computeAll,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
closedConclusion,
baseApply,
baseClosed,
promote_hyp,
pointwiseFunctionality,
unionElimination,
dependent_functionElimination,
rename,
setElimination,
applyLambdaEquality,
equalitySymmetry,
equalityTransitivity,
natural_numberEquality,
addEquality,
dependent_set_memberEquality,
hypothesisEquality,
cumulativity,
isectElimination,
productEquality,
thin,
productElimination,
sqequalHypSubstitution,
independent_pairFormation,
lambdaFormation,
isect_memberFormation,
hypothesis,
extract_by_obid,
introduction,
cut,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution,
lambdaFormation_alt,
Error :memTop,
dependent_pairFormation_alt,
lambdaEquality_alt,
dependent_set_memberEquality_alt,
approximateComputation,
universeIsType,
productIsType,
imageElimination,
functionIsType,
functionExtensionality,
inhabitedIsType,
equalityIstype
Latex:
\mforall{}[T:Type]. \mforall{}L1,L:T List. (interleaving(T;[];L1;L) \mLeftarrow{}{}\mRightarrow{} L = L1)
Date html generated:
2020_05_20-AM-07_48_18
Last ObjectModification:
2020_01_07-PM-02_28_50
Theory : list!
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