Nuprl Lemma : term-cases
∀[opr:Type]
  ∀t:term(opr)
    ((∃v:varname(). ((¬(v = nullvar() ∈ varname())) ∧ (t = varterm(v) ∈ term(opr))))
    ∨ (∃f:opr. ∃bts:{bt:bound-term(opr)| bound-term-size(bt) < term-size(t)}  List. (t = mkterm(f;bts) ∈ term(opr))))
Proof
Definitions occuring in Statement : 
bound-term-size: bound-term-size(bt)
, 
bound-term: bound-term(opr)
, 
term-size: term-size(t)
, 
mkterm: mkterm(opr;bts)
, 
varterm: varterm(v)
, 
term: term(opr)
, 
nullvar: nullvar()
, 
varname: varname()
, 
list: T List
, 
less_than: a < b
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
exists: ∃x:A. B[x]
, 
not: ¬A
, 
or: P ∨ Q
, 
and: P ∧ Q
, 
set: {x:A| B[x]} 
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
uimplies: b supposing a
, 
implies: P 
⇒ Q
, 
coterm-fun: coterm-fun(opr;T)
, 
or: P ∨ Q
, 
exists: ∃x:A. B[x]
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
not: ¬A
, 
false: False
, 
varterm: varterm(v)
, 
nat: ℕ
, 
prop: ℙ
, 
bound-term: bound-term(opr)
, 
mkterm: mkterm(opr;bts)
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
bound-term-size: bound-term-size(bt)
, 
sq_stable: SqStable(P)
, 
decidable: Dec(P)
, 
ge: i ≥ j 
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
squash: ↓T
, 
le: A ≤ B
Lemmas referenced : 
term-ext, 
subtype_rel_weakening, 
term_wf, 
coterm-fun_wf, 
ext-eq_inversion, 
nullvar_wf, 
varterm_wf, 
istype-void, 
list_wf, 
bound-term_wf, 
less_than_wf, 
bound-term-size_wf, 
term-size_wf, 
mkterm_wf, 
subtype_rel_list, 
varname_wf, 
istype-less_than, 
list-subtype, 
l_member_wf, 
subtype_rel_sets, 
term_size_mkterm_lemma, 
istype-universe, 
summand-le-lsum, 
sq_stable__le, 
decidable__le, 
nat_properties, 
full-omega-unsat, 
intformand_wf, 
intformle_wf, 
itermConstant_wf, 
itermVar_wf, 
intformnot_wf, 
istype-int, 
int_formula_prop_and_lemma, 
int_formula_prop_le_lemma, 
int_term_value_constant_lemma, 
int_term_value_var_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_wf, 
decidable__lt, 
lsum_wf, 
intformless_wf, 
itermAdd_wf, 
int_formula_prop_less_lemma, 
int_term_value_add_lemma
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
lambdaFormation_alt, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
applyEquality, 
hypothesis, 
independent_isectElimination, 
sqequalRule, 
inhabitedIsType, 
unionElimination, 
inlFormation_alt, 
dependent_pairFormation_alt, 
setElimination, 
rename, 
independent_functionElimination, 
voidElimination, 
equalityIstype, 
because_Cache, 
independent_pairFormation, 
productIsType, 
functionIsType, 
equalityTransitivity, 
equalitySymmetry, 
universeIsType, 
setEquality, 
lambdaEquality_alt, 
productEquality, 
setIsType, 
productElimination, 
inrFormation_alt, 
dependent_functionElimination, 
Error :memTop, 
instantiate, 
universeEquality, 
natural_numberEquality, 
applyLambdaEquality, 
approximateComputation, 
int_eqEquality, 
imageMemberEquality, 
baseClosed, 
imageElimination, 
dependent_set_memberEquality_alt, 
addEquality
Latex:
\mforall{}[opr:Type]
    \mforall{}t:term(opr)
        ((\mexists{}v:varname().  ((\mneg{}(v  =  nullvar()))  \mwedge{}  (t  =  varterm(v))))
        \mvee{}  (\mexists{}f:opr
                \mexists{}bts:\{bt:bound-term(opr)|  bound-term-size(bt)  <  term-size(t)\}    List.  (t  =  mkterm(f;bts))))
Date html generated:
2020_05_19-PM-09_54_00
Last ObjectModification:
2020_03_09-PM-04_08_27
Theory : terms
Home
Index