Nuprl Lemma : var-num_wf
∀[t:Atom]. ∀[b:varname()]. (var-num(t;b) ∈ {-1...})
Proof
Definitions occuring in Statement :
var-num: var-num(t;b),
varname: varname(),
int_upper: {i...},
uall: ∀[x:A]. B[x],
member: t ∈ T,
minus: -n,
natural_number: $n,
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
varname: varname(),
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
var-num: var-num(t;b),
pi2: snd(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
int_upper: {i...},
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
false: False,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
nat: ℕ,
ge: i ≥ j
Lemmas referenced :
eq_atom_wf,
eqtt_to_assert,
assert_of_eq_atom,
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-le,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
nat_properties,
intformand_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
varname_wf,
istype-atom
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
imageElimination,
productElimination,
thin,
unionElimination,
equalityElimination,
sqequalRule,
isatomReduceTrue,
hypothesisEquality,
extract_by_obid,
isectElimination,
hypothesis,
inhabitedIsType,
lambdaFormation_alt,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
because_Cache,
dependent_set_memberEquality_alt,
natural_numberEquality,
dependent_functionElimination,
minusEquality,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
Error :memTop,
universeIsType,
voidElimination,
equalityIstype,
promote_hyp,
instantiate,
cumulativity,
addEquality,
setElimination,
rename,
int_eqEquality,
independent_pairFormation,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[t:Atom]. \mforall{}[b:varname()]. (var-num(t;b) \mmember{} \{-1...\})
Date html generated:
2020_05_19-PM-09_53_13
Last ObjectModification:
2020_03_09-PM-04_08_02
Theory : terms
Home
Index