Nuprl Lemma : maybe_new_var_wf
∀[v:varname()]. ∀[vs:varname() List]. (maybe_new_var(v;vs) ∈ varname())
Proof
Definitions occuring in Statement :
maybe_new_var: maybe_new_var(v;vs),
varname: varname(),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
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 ,
maybe_new_var: maybe_new_var(v;vs),
pi2: snd(t),
all: ∀x:A. B[x],
or: P ∨ Q,
btrue: tt,
subtype_rel: A ⊆r B,
cons: [a / b],
bfalse: ff,
has-value: (a)↓,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
ge: i ≥ j ,
decidable: Dec(P),
false: False,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
it: ⋅,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
nat: ℕ,
pi1: fst(t)
Lemmas referenced :
varname_wf,
list-cases,
null_nil_lemma,
product_subtype_list,
null_cons_lemma,
value-type-has-value,
atom-value-type,
list-max_wf,
var-num_wf,
cons_wf,
length_of_cons_lemma,
non_neg_length,
decidable__lt,
length_wf,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
lt_int_wf,
subtype_rel_b-union-left,
nat_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
less_than_wf,
assert_of_lt_int,
istype-less_than,
bfalse_wf,
decidable__le,
istype-le,
ifthenelse_wf,
nat_properties,
subtype_rel_b-union-right,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
imageElimination,
productElimination,
thin,
unionElimination,
equalityElimination,
sqequalRule,
isatomReduceTrue,
hypothesisEquality,
introduction,
extract_by_obid,
hypothesis,
isectElimination,
dependent_functionElimination,
applyEquality,
because_Cache,
promote_hyp,
hypothesis_subsumption,
Error :memTop,
callbyvalueReduce,
atomEquality,
independent_isectElimination,
lambdaEquality_alt,
inhabitedIsType,
natural_numberEquality,
addEquality,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
independent_pairFormation,
universeIsType,
voidElimination,
lambdaFormation_alt,
closedConclusion,
productEquality,
equalityTransitivity,
equalitySymmetry,
equalityIstype,
instantiate,
cumulativity,
imageMemberEquality,
dependent_pairEquality_alt,
independent_pairEquality,
dependent_set_memberEquality_alt,
universeEquality,
baseClosed,
setElimination,
rename
Latex:
\mforall{}[v:varname()]. \mforall{}[vs:varname() List]. (maybe\_new\_var(v;vs) \mmember{} varname())
Date html generated:
2020_05_19-PM-09_53_15
Last ObjectModification:
2020_03_09-PM-04_08_03
Theory : terms
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