Nuprl Lemma : permute-to-front-permutation
∀[T:Type]. ∀L:T List. ∀idxs:ℕ List. permutation(T;L;permute-to-front(L;idxs))
Proof
Definitions occuring in Statement :
permute-to-front: permute-to-front(L;idxs),
permutation: permutation(T;L1;L2),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
permute-to-front: permute-to-front(L;idxs),
permutation: permutation(T;L1;L2),
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
int_seg: {i..j-},
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nat: ℕ,
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
cand: A c∧ B,
sq_type: SQType(T),
le: A ≤ B,
less_than': less_than'(a;b),
uiff: uiff(P;Q),
l_disjoint: l_disjoint(T;l1;l2)
Lemmas referenced :
list_wf,
nat_wf,
select_wf,
int_seg_wf,
append_wf,
filter_wf5,
upto_wf,
l_member_wf,
length_wf,
int-list-member_wf,
subtype_rel_list,
bnot_wf,
int_seg_properties,
decidable__le,
satisfiable-full-omega-tt,
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,
length-append,
less_than_wf,
squash_wf,
true_wf,
length_upto,
length_wf_nat,
filter-split-length,
iff_weakening_equal,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
permute_list_wf,
equal_wf,
subtype_base_sq,
list_subtype_base,
set_subtype_base,
lelt_wf,
int_subtype_base,
no_repeats_inject,
int_seg_subtype,
false_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
no_repeats_append_iff,
no_repeats_filter,
no_repeats_upto,
member_filter,
assert_wf,
not_wf,
assert-int-list-member,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
inject_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
dependent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
cumulativity,
hypothesisEquality,
universeEquality,
lambdaEquality,
natural_numberEquality,
because_Cache,
setElimination,
rename,
dependent_functionElimination,
applyEquality,
intEquality,
independent_isectElimination,
sqequalRule,
setEquality,
productElimination,
unionElimination,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
independent_functionElimination,
instantiate,
productEquality,
impliesFunctionality,
functionExtensionality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}idxs:\mBbbN{} List. permutation(T;L;permute-to-front(L;idxs))
Date html generated:
2018_05_21-PM-07_32_07
Last ObjectModification:
2017_07_26-PM-05_07_17
Theory : general
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