Nuprl Lemma : append_interleaving
∀[T:Type]. ∀L1,L2:T List. interleaving(T;L1;L2;L1 @ L2)
Proof
Definitions occuring in Statement :
interleaving: interleaving(T;L1;L2;L),
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
interleaving: interleaving(T;L1;L2;L),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
false: False,
uiff: uiff(P;Q),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
increasing: increasing(f;k),
int_seg: {i..j-},
lelt: i ≤ j < k,
disjoint_sublists: disjoint_sublists(T;L1;L2;L),
le: A ≤ B,
less_than: a < b,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
le_wf,
squash_wf,
true_wf,
length_append,
subtype_rel_list,
top_wf,
subtype_rel_self,
iff_weakening_equal,
add_nat_wf,
length_wf_nat,
nat_wf,
nat_properties,
decidable__le,
add-is-int-iff,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
intformeq_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_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
false_wf,
equal_wf,
list_wf,
length-append,
int_seg_properties,
subtract_wf,
length_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
int_seg_wf,
non_neg_length,
append_wf,
lelt_wf,
add-member-int_seg2,
itermSubtract_wf,
int_term_value_subtract_lemma,
id_increasing,
select_append_front,
select_wf,
select_append_back,
add-subtract-cancel,
increasing_wf,
all_wf,
not_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
lambdaFormation,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
intEquality,
natural_numberEquality,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
productElimination,
independent_functionElimination,
applyLambdaEquality,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
approximateComputation,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
dependent_set_memberEquality,
universeIsType,
addEquality,
cumulativity,
productEquality,
functionExtensionality,
functionEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. interleaving(T;L1;L2;L1 @ L2)
Date html generated:
2019_10_15-AM-10_57_07
Last ObjectModification:
2018_09_27-AM-10_30_58
Theory : list!
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