Nuprl Lemma : append_functionality_wrt_permutation
∀[A:Type]
∀as1,as2,bs1,bs2:A List. (permutation(A;as1;bs1) ⇒ permutation(A;as2;bs2) ⇒ permutation(A;as1 @ as2;bs1 @ bs2))
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uimplies: b supposing a,
permutation: permutation(T;L1;L2),
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
top: Top,
int_seg: {i..j-},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T},
not: ¬A,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
subtype_rel: A ⊆r B,
less_than: a < b,
le: A ≤ B,
lelt: i ≤ j < k,
less_than': less_than'(a;b),
inject: Inj(A;B;f),
nat: ℕ,
squash: ↓T,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
true: True,
cand: A c∧ B
Lemmas referenced :
permutation-length,
permutation_wf,
list_wf,
length-append,
bnot_wf,
le_wf,
le_int_wf,
less_than_wf,
assert_wf,
equal-wf-T-base,
bool_wf,
length_wf,
lt_int_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
equal_wf,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
non_neg_length,
int_seg_subtype,
lelt_wf,
int_seg_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
add-member-int_seg1,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_term_value_subtract_lemma,
itermSubtract_wf,
subtract_wf,
inject_wf,
append_wf,
permute_list_wf,
subtype_rel_function,
false_wf,
length_append,
subtype_rel_list,
top_wf,
full-omega-unsat,
nat_properties,
length_wf_nat,
decidable__equal_int,
add-is-int-iff,
list_extensionality,
nat_wf,
iff_weakening_equal,
add_functionality_wrt_eq,
true_wf,
squash_wf,
permute_list_length,
select_wf,
permute_list_select,
subtype_rel_self,
select_append_front,
select_append_back,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
because_Cache,
productElimination,
universeEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
lambdaEquality,
baseClosed,
equalitySymmetry,
equalityTransitivity,
cumulativity,
rename,
setElimination,
unionElimination,
equalityElimination,
independent_functionElimination,
dependent_functionElimination,
computeAll,
intEquality,
int_eqEquality,
dependent_pairFormation,
applyLambdaEquality,
addEquality,
independent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
functionExtensionality,
applyEquality,
productEquality,
approximateComputation,
imageElimination,
closedConclusion,
baseApply,
promote_hyp,
pointwiseFunctionality,
imageMemberEquality,
instantiate,
hyp_replacement
Latex:
\mforall{}[A:Type]
\mforall{}as1,as2,bs1,bs2:A List.
(permutation(A;as1;bs1) {}\mRightarrow{} permutation(A;as2;bs2) {}\mRightarrow{} permutation(A;as1 @ as2;bs1 @ bs2))
Date html generated:
2019_06_20-PM-01_37_49
Last ObjectModification:
2018_08_21-PM-11_00_37
Theory : list_1
Home
Index