Nuprl Lemma : maybe_new_var-distinct
∀[a:varname()]. ∀[vs:varname() List]. (∀v∈vs.¬(maybe_new_var(a;vs) = v ∈ varname()))
Proof
Definitions occuring in Statement :
maybe_new_var: maybe_new_var(v;vs),
varname: varname(),
l_all: (∀x∈L.P[x]),
list: T List,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = 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 ,
pi2: snd(t),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
nat: ℕ,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
maybe_new_var: maybe_new_var(v;vs),
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
pi1: fst(t),
has-value: (a)↓,
cons: [a / b],
le: A ≤ B,
cand: A c∧ B,
decidable: Dec(P),
subtract: n - m,
less_than': less_than'(a;b),
true: True,
int_upper: {i...},
l_all: (∀x∈L.P[x]),
squash: ↓T,
var-num: var-num(t;b),
satisfiable_int_formula: satisfiable_int_formula(fmla),
ge: i ≥ j
Lemmas referenced :
atom_subtype_base,
product_subtype_base,
nat_wf,
istype-atom,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
l_all_iff,
varname_wf,
not_wf,
equal_wf,
maybe_new_var_wf,
l_member_wf,
null_wf,
eqtt_to_assert,
assert_of_null,
length_wf,
length_of_nil_lemma,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
equal-wf-T-base,
list_wf,
nil_wf,
value-type-has-value,
atom-value-type,
list-max-property,
var-num_wf,
list-cases,
product_subtype_list,
length_of_cons_lemma,
length_wf_nat,
decidable__lt,
istype-false,
not-lt-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
list-max_wf,
l_all_wf,
squash_wf,
true_wf,
istype-int_upper,
subtype_rel_self,
iff_weakening_equal,
lt_int_wf,
assert_of_lt_int,
less_than_wf,
istype-less_than,
eq_atom_wf,
equal-wf-base,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
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,
istype-le,
bnot_wf,
eq_atom-reflexive,
istype-assert,
istype-void,
itermAdd_wf,
int_term_value_add_lemma,
nat_properties,
uiff_transitivity,
assert_of_eq_atom,
iff_transitivity,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
imageElimination,
productElimination,
thin,
unionElimination,
equalityElimination,
sqequalRule,
hypothesisEquality,
applyEquality,
extract_by_obid,
hypothesis,
isectElimination,
atomEquality,
lambdaEquality_alt,
independent_isectElimination,
lambdaFormation_alt,
intEquality,
natural_numberEquality,
dependent_functionElimination,
setElimination,
rename,
setIsType,
inhabitedIsType,
universeIsType,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
applyLambdaEquality,
dependent_set_memberEquality_alt,
independent_pairFormation,
productIsType,
equalityIstype,
voidElimination,
dependent_pairFormation_alt,
promote_hyp,
instantiate,
cumulativity,
baseClosed,
isatomReduceTrue,
callbyvalueReduce,
hypothesis_subsumption,
Error :memTop,
addEquality,
minusEquality,
baseApply,
closedConclusion,
sqequalBase,
functionIsTypeImplies,
isect_memberEquality_alt,
isectIsTypeImplies,
imageMemberEquality,
universeEquality,
approximateComputation,
int_eqEquality,
functionIsType
Latex:
\mforall{}[a:varname()]. \mforall{}[vs:varname() List]. (\mforall{}v\mmember{}vs.\mneg{}(maybe\_new\_var(a;vs) = v))
Date html generated:
2020_05_19-PM-09_53_17
Last ObjectModification:
2020_03_09-PM-04_08_03
Theory : terms
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