Nuprl Lemma : sq_stable__alpha-aux
∀[opr:Type]. ∀a,b:term(opr). ∀vs,ws:varname() List.  SqStable(alpha-aux(opr;vs;ws;a;b))
Proof
Definitions occuring in Statement : 
alpha-aux: alpha-aux(opr;vs;ws;a;b)
, 
term: term(opr)
, 
varname: varname()
, 
list: T List
, 
sq_stable: SqStable(P)
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
so_apply: x[s]
, 
implies: P 
⇒ Q
, 
uimplies: b supposing a
, 
not: ¬A
, 
false: False
, 
alpha-aux: alpha-aux(opr;vs;ws;a;b)
, 
varterm: varterm(v)
, 
mkterm: mkterm(opr;bts)
, 
bound-term: bound-term(opr)
, 
pi2: snd(t)
, 
guard: {T}
, 
nil: []
, 
it: ⋅
, 
or: P ∨ Q
, 
cons: [a / b]
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
sq_stable: SqStable(P)
, 
subtype_rel: A ⊆r B
, 
nat: ℕ
, 
l_member: (x ∈ l)
, 
exists: ∃x:A. B[x]
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
select: L[n]
, 
cand: A c∧ B
, 
nat_plus: ℕ+
, 
decidable: Dec(P)
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
uiff: uiff(P;Q)
, 
ge: i ≥ j 
Lemmas referenced : 
term-induction, 
term_wf, 
list_wf, 
varname_wf, 
sq_stable_wf, 
alpha-aux_wf, 
all_wf, 
varterm_wf, 
sq_stable_from_decidable, 
assert_wf, 
same-binding_wf, 
decidable__assert, 
false_wf, 
decidable__false, 
bound-term_wf, 
l_member_wf, 
nullvar_wf, 
istype-void, 
mkterm_wf, 
list_induction, 
list-cases, 
sq_stable__equal, 
product_subtype_list, 
nil_wf, 
cons_member, 
cons_wf, 
spread_cons_lemma, 
sq_stable__and, 
equal-wf-base, 
length_wf_nat, 
set_subtype_base, 
le_wf, 
istype-int, 
int_subtype_base, 
rev-append_wf, 
istype-universe, 
istype-le, 
length_of_cons_lemma, 
add_nat_plus, 
decidable__lt, 
full-omega-unsat, 
intformnot_wf, 
intformless_wf, 
itermConstant_wf, 
int_formula_prop_not_lemma, 
int_formula_prop_less_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_wf, 
istype-less_than, 
nat_plus_properties, 
add-is-int-iff, 
intformand_wf, 
itermVar_wf, 
itermAdd_wf, 
intformeq_wf, 
int_formula_prop_and_lemma, 
int_term_value_var_lemma, 
int_term_value_add_lemma, 
int_formula_prop_eq_lemma, 
length_wf, 
select_wf, 
nat_properties, 
decidable__le, 
intformle_wf, 
int_formula_prop_le_lemma
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
sqequalRule, 
lambdaEquality_alt, 
functionEquality, 
hypothesis, 
universeIsType, 
independent_functionElimination, 
lambdaFormation_alt, 
because_Cache, 
setElimination, 
rename, 
independent_isectElimination, 
voidElimination, 
inhabitedIsType, 
dependent_functionElimination, 
functionIsType, 
equalityIstype, 
productElimination, 
setIsType, 
unionElimination, 
promote_hyp, 
hypothesis_subsumption, 
inrFormation_alt, 
productEquality, 
independent_pairEquality, 
Error :memTop, 
functionIsTypeImplies, 
spreadEquality, 
intEquality, 
applyEquality, 
natural_numberEquality, 
isect_memberEquality_alt, 
productIsType, 
sqequalBase, 
equalitySymmetry, 
instantiate, 
universeEquality, 
dependent_pairFormation_alt, 
dependent_set_memberEquality_alt, 
independent_pairFormation, 
approximateComputation, 
equalityTransitivity, 
applyLambdaEquality, 
pointwiseFunctionality, 
baseApply, 
closedConclusion, 
baseClosed, 
int_eqEquality
Latex:
\mforall{}[opr:Type].  \mforall{}a,b:term(opr).  \mforall{}vs,ws:varname()  List.    SqStable(alpha-aux(opr;vs;ws;a;b))
Date html generated:
2020_05_19-PM-09_55_25
Last ObjectModification:
2020_03_09-PM-04_08_53
Theory : terms
Home
Index