Nuprl Lemma : nil-at
∀[ms:colist(ℕ)]. ([]@ms ~ [])
Proof
Definitions occuring in Statement :
list-at: L1@L2,
nil: [],
colist: colist(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uimplies: b supposing a,
nil: [],
top: Top,
bfalse: ff,
cons: [a / b],
nat: ℕ,
false: False,
ge: i ≥ j ,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
list-at: L1@L2,
ifthenelse: if b then t else f fi
Lemmas referenced :
colist-ext,
nat_wf,
isaxiom_wf_listunion,
colist_wf,
subtype_rel_b-union-left,
unit_wf2,
axiom-listunion,
list_at_nil2_lemma,
istype-void,
subtype_rel_b-union-right,
non-axiom-listunion,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
istype-less_than,
null_cons_lemma,
null_nil_lemma,
reduce_hd_cons_lemma,
reduce_tl_nil_lemma,
reduce_tl_cons_lemma,
subtract-1-ge-0
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
promote_hyp,
productElimination,
hypothesis_subsumption,
hypothesisEquality,
applyEquality,
sqequalRule,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
unionElimination,
equalityElimination,
productEquality,
independent_isectElimination,
dependent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination,
rename,
Error :equalityIstype,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
axiomSqEquality,
Error :universeIsType,
setElimination,
intWeakElimination,
natural_numberEquality,
approximateComputation,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
int_eqEquality,
independent_pairFormation,
Error :functionIsTypeImplies,
because_Cache
Latex:
\mforall{}[ms:colist(\mBbbN{})]. ([]@ms \msim{} [])
Date html generated:
2019_06_20-PM-01_21_03
Last ObjectModification:
2018_12_04-AM-11_51_32
Theory : list_1
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