Nuprl Lemma : list_decomp_rev_wf
∀[T:Type]. ∀[l:T List]. list_decomp_rev{i:l}(l) ∈ {p:T × (T List)| l = ((snd(p)) @ [fst(p)]) ∈ (T List)} supposing 0 <\000C ||l||
Proof
Definitions occuring in Statement :
list_decomp_rev: list_decomp_rev{i:l}(l),
length: ||as||,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
member: t ∈ T,
set: {x:A| B[x]} ,
product: 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,
uimplies: b supposing a,
list_decomp_rev: list_decomp_rev{i:l}(l),
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
pi2: snd(t),
pi1: fst(t),
and: P ∧ Q,
squash: ↓T,
true: True
Lemmas referenced :
list_decomp_reverse,
uall_wf,
all_wf,
list_wf,
isect_wf,
less_than_wf,
length_wf,
exists_wf,
equal_wf,
append_wf,
cons_wf,
nil_wf,
uimplies_subtype,
and_wf,
squash_wf,
true_wf,
pi2_wf,
pi1_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
universeEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesisEquality,
natural_numberEquality,
because_Cache,
applyEquality,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
isectEquality,
functionEquality,
independent_isectElimination,
productElimination,
dependent_set_memberEquality,
independent_pairFormation,
applyLambdaEquality,
setElimination,
rename,
imageElimination,
imageMemberEquality,
baseClosed,
independent_pairEquality,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. list\_decomp\_rev\{i:l\}(l) \mmember{} \{p:T \mtimes{} (T List)| l = ((snd(p)) @ [fst(p)])\} supp\000Cosing 0 < ||l||
Date html generated:
2017_04_17-AM-08_43_26
Last ObjectModification:
2017_02_27-PM-05_02_27
Theory : list_1
Home
Index