Nuprl Lemma : list_split_one_one
∀[T:Type]. ∀[f:(T List) ⟶ 𝔹]. ∀[X,Y:T List].
X = Y ∈ (T List) supposing list_split(f;X) = list_split(f;Y) ∈ (T List List × (T List))
Proof
Definitions occuring in Statement :
list_split: list_split(f;L),
list: T List,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
top: Top,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
pi2: snd(t)
Lemmas referenced :
list_split_inverse,
list_split_wf,
list_wf,
set_wf,
is_list_splitting_wf,
pi1_wf_top,
subtype_rel_product,
top_wf,
equal_wf,
pi2_wf,
squash_wf,
true_wf,
pair_eta_rw,
iff_weakening_equal,
bool_wf,
append_wf,
concat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
cumulativity,
functionExtensionality,
applyEquality,
hypothesis,
productEquality,
sqequalRule,
lambdaEquality,
spreadEquality,
productElimination,
independent_pairEquality,
lambdaFormation,
setElimination,
rename,
because_Cache,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
setEquality,
axiomEquality,
functionEquality
Latex:
\mforall{}[T:Type]. \mforall{}[f:(T List) {}\mrightarrow{} \mBbbB{}]. \mforall{}[X,Y:T List]. X = Y supposing list\_split(f;X) = list\_split(f;Y)
Date html generated:
2018_05_21-PM-08_05_37
Last ObjectModification:
2017_07_26-PM-05_41_36
Theory : general
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