Nuprl Lemma : list-at-at
∀ms,ns:colist(ℕ). ∀[T:Type]. ∀[L:colist(T)]. (L@ns@ms = L@combine-skips(ns;ms;0) ∈ colist(T))
Proof
Definitions occuring in Statement :
combine-skips: combine-skips(as;bs;n),
list-at: L1@L2,
colist: colist(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
prop: ℙ,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
false: False,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
nth_tl: nth_tl(n;as),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
list-at_wf,
list-at-combine-skips,
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-le,
subtype_rel_self,
iff_weakening_equal,
colist_wf,
istype-universe,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
Error :isect_memberFormation_alt,
introduction,
cut,
applyEquality,
thin,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
Error :universeIsType,
Error :inhabitedIsType,
because_Cache,
Error :dependent_set_memberEquality_alt,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :isect_memberEquality_alt,
voidElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
productElimination,
axiomEquality,
Error :isectIsTypeImplies,
universeEquality
Latex:
\mforall{}ms,ns:colist(\mBbbN{}). \mforall{}[T:Type]. \mforall{}[L:colist(T)]. (L@ns@ms = L@combine-skips(ns;ms;0))
Date html generated:
2019_06_20-PM-01_21_50
Last ObjectModification:
2018_12_07-PM-06_29_20
Theory : list_1
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