Nuprl Lemma : nil_interleaving2
∀[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 :
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,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
prop: ℙ,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
false: False,
le: A ≤ B,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
squash: ↓T,
true: True,
guard: {T},
uiff: uiff(P;Q),
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,
less_than': less_than'(a;b)
Lemmas referenced :
length_of_nil_lemma,
istype-nat,
length_wf_nat,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
length_wf,
disjoint_sublists_wf,
nil_wf,
non_neg_length,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
list_wf,
subtype_rel_self,
iff_weakening_equal,
add-zero,
istype-le,
disjoint_sublists_sublist,
proper_sublist_length,
nat_properties,
decidable__equal_int,
add-is-int-iff,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
false_wf,
stuck-spread,
istype-base,
int_seg_wf,
int_seg_properties,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
istype-less_than,
id_increasing,
select_wf,
istype-void,
increasing_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
hypothesis,
isect_memberFormation_alt,
lambdaFormation_alt,
independent_pairFormation,
sqequalHypSubstitution,
productElimination,
thin,
productIsType,
equalityIstype,
isectElimination,
hypothesisEquality,
applyEquality,
intEquality,
lambdaEquality_alt,
natural_numberEquality,
independent_isectElimination,
addEquality,
sqequalBase,
equalitySymmetry,
universeIsType,
dependent_functionElimination,
because_Cache,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
Error :memTop,
voidElimination,
dependent_set_memberEquality_alt,
imageElimination,
equalityTransitivity,
instantiate,
universeEquality,
imageMemberEquality,
baseClosed,
inhabitedIsType,
applyLambdaEquality,
setElimination,
rename,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
functionIsType,
functionExtensionality,
hyp_replacement
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_20
Last ObjectModification:
2020_01_22-PM-03_32_07
Theory : list!
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