Nuprl Lemma : permute-to-front_wf
∀[T:Type]. ∀[L:T List]. ∀[idxs:ℕ List]. (permute-to-front(L;idxs) ∈ T List)
Proof
Definitions occuring in Statement :
permute-to-front: permute-to-front(L;idxs),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
permute-to-front: permute-to-front(L;idxs),
all: ∀x:A. B[x],
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),
exists: ∃x:A. B[x],
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
Lemmas referenced :
list_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
iff_weakening_equal,
filter-split-length,
length_wf_nat,
length_upto,
true_wf,
squash_wf,
less_than_wf,
length-append,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
bnot_wf,
nat_wf,
subtype_rel_list,
int-list-member_wf,
length_wf,
l_member_wf,
upto_wf,
filter_wf5,
append_wf,
int_seg_wf,
select_wf,
permute_list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
natural_numberEquality,
because_Cache,
hypothesis,
lambdaFormation,
setElimination,
rename,
dependent_functionElimination,
applyEquality,
intEquality,
independent_isectElimination,
setEquality,
productElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
universeEquality,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[idxs:\mBbbN{} List]. (permute-to-front(L;idxs) \mmember{} T List)
Date html generated:
2016_05_15-PM-04_23_24
Last ObjectModification:
2016_01_16-AM-11_12_20
Theory : general
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