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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