Nuprl Lemma : maybe_new_var-is-null
∀a:varname(). ∀[vs:varname() List]. a = nullvar() ∈ varname() supposing maybe_new_var(a;vs) = nullvar() ∈ varname()
Proof
Definitions occuring in Statement : 
nullvar: nullvar()
, 
maybe_new_var: maybe_new_var(v;vs)
, 
varname: varname()
, 
list: T List
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
maybe_new_var: maybe_new_var(v;vs)
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
false: False
, 
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]
, 
nat: ℕ
, 
pi1: fst(t)
, 
has-value: (a)↓
, 
or: P ∨ Q
, 
cons: [a / b]
, 
guard: {T}
, 
and: P ∧ Q
, 
le: A ≤ B
, 
cand: A c∧ B
, 
decidable: Dec(P)
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
uiff: uiff(P;Q)
, 
subtract: n - m
, 
less_than': less_than'(a;b)
, 
true: True
, 
prop: ℙ
, 
int_upper: {i...}
, 
sq_type: SQType(T)
, 
btrue: tt
, 
bfalse: ff
, 
nullvar: nullvar()
Lemmas referenced : 
maybe_new_var_wf, 
nullvar_wf, 
list_wf, 
varname_wf, 
null_wf, 
assert_wf, 
bnot_wf, 
not_wf, 
equal-wf-T-base, 
nil_wf, 
istype-assert, 
istype-void, 
length_wf, 
length_of_nil_lemma, 
atom_subtype_base, 
product_subtype_base, 
nat_wf, 
istype-atom, 
set_subtype_base, 
le_wf, 
istype-int, 
int_subtype_base, 
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_member_wf, 
l_all_wf, 
bool_cases, 
subtype_base_sq, 
bool_wf, 
bool_subtype_base, 
eqtt_to_assert, 
assert_of_null, 
eqff_to_assert, 
iff_transitivity, 
iff_weakening_uiff, 
assert_of_bnot, 
lt_int_wf, 
less_than_wf, 
istype-less_than, 
assert_of_lt_int
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation_alt, 
isect_memberFormation_alt, 
introduction, 
cut, 
sqequalHypSubstitution, 
hypothesis, 
equalityIstype, 
inhabitedIsType, 
hypothesisEquality, 
extract_by_obid, 
isectElimination, 
thin, 
sqequalRule, 
isect_memberEquality_alt, 
axiomEquality, 
isectIsTypeImplies, 
universeIsType, 
because_Cache, 
equalityTransitivity, 
equalitySymmetry, 
baseClosed, 
functionIsType, 
applyLambdaEquality, 
imageElimination, 
productElimination, 
unionElimination, 
equalityElimination, 
applyEquality, 
atomEquality, 
lambdaEquality_alt, 
independent_isectElimination, 
intEquality, 
natural_numberEquality, 
isatomReduceTrue, 
callbyvalueReduce, 
dependent_functionElimination, 
independent_functionElimination, 
voidElimination, 
promote_hyp, 
hypothesis_subsumption, 
Error :memTop, 
setElimination, 
rename, 
independent_pairFormation, 
addEquality, 
minusEquality, 
baseApply, 
closedConclusion, 
sqequalBase, 
productIsType, 
setIsType, 
instantiate, 
cumulativity, 
tokenEquality
Latex:
\mforall{}a:varname().  \mforall{}[vs:varname()  List].  a  =  nullvar()  supposing  maybe\_new\_var(a;vs)  =  nullvar()
Date html generated:
2020_05_19-PM-09_53_21
Last ObjectModification:
2020_03_09-PM-04_08_04
Theory : terms
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