Nuprl Lemma : permute_permute_list
∀[T:Type]. ∀[L:T List]. ∀[f,g:ℕ||L|| ⟶ ℕ||L||]. (((L o f) o g) = (L o f o g) ∈ (T List))
Proof
Definitions occuring in Statement :
permute_list: (L o f),
length: ||as||,
list: T List,
compose: f o g,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x],
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
list_wf,
permute_list_wf,
int_seg_wf,
length_wf,
subtype_rel_dep_function,
int_seg_subtype,
false_wf,
permute_list_length,
le_reflexive,
permute_list-compose,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
cumulativity,
because_Cache,
functionExtensionality,
natural_numberEquality,
sqequalRule,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
dependent_functionElimination,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
functionEquality,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[f,g:\mBbbN{}||L|| {}\mrightarrow{} \mBbbN{}||L||]. (((L o f) o g) = (L o f o g))
Date html generated:
2017_04_17-AM-08_10_10
Last ObjectModification:
2017_02_27-PM-04_37_43
Theory : list_1
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