Nuprl Lemma : permutation-map
∀[A:Type]. ∀L1,L2:A List. (permutation(A;L1;L2) ⇒ (∀[B:Type]. ∀f:A ⟶ B. permutation(B;map(f;L1);map(f;L2))))
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
permutation: permutation(T;L1;L2),
exists: ∃x:A. B[x],
member: t ∈ T,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
nat: ℕ,
cand: A c∧ B,
int_seg: {i..j-},
lelt: i ≤ j < k,
ge: i ≥ j
Lemmas referenced :
subtype_rel_dep_function,
int_seg_wf,
length_wf,
map_wf,
int_seg_subtype,
false_wf,
le_wf,
map_length_nat,
iff_weakening_equal,
decidable__le,
satisfiable-full-omega-tt,
intformnot_wf,
intformle_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
list_extensionality,
permute_list_wf,
map-length,
less_than_wf,
nat_wf,
equal_wf,
list_wf,
inject_wf,
permutation_wf,
permute_list_length,
lelt_wf,
select_wf,
non_neg_length,
nat_properties,
length_wf_nat,
int_seg_properties,
intformand_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_term_value_constant_lemma,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
length-map,
map_select,
permute_list_select
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
cut,
hypothesisEquality,
applyEquality,
introduction,
extract_by_obid,
isectElimination,
natural_numberEquality,
cumulativity,
hypothesis,
sqequalRule,
lambdaEquality,
functionExtensionality,
independent_isectElimination,
because_Cache,
independent_pairFormation,
imageElimination,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
dependent_functionElimination,
unionElimination,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
promote_hyp,
setElimination,
rename,
hyp_replacement,
applyLambdaEquality,
productEquality,
functionEquality,
universeEquality,
dependent_set_memberEquality
Latex:
\mforall{}[A:Type]
\mforall{}L1,L2:A List.
(permutation(A;L1;L2) {}\mRightarrow{} (\mforall{}[B:Type]. \mforall{}f:A {}\mrightarrow{} B. permutation(B;map(f;L1);map(f;L2))))
Date html generated:
2017_04_17-AM-08_24_31
Last ObjectModification:
2017_02_27-PM-04_47_19
Theory : list_1
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