Nuprl Lemma : intformless_wf
∀[left,right:int_term()].  ((left "<" right) ∈ int_formula())
Proof
Definitions occuring in Statement : 
intformless: (left "<" right)
, 
int_formula: int_formula()
, 
int_term: int_term()
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
int_formula: int_formula()
, 
intformless: (left "<" right)
, 
eq_atom: x =a y
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
subtype_rel: A ⊆r B
, 
ext-eq: A ≡ B
, 
and: P ∧ Q
, 
int_formulaco_size: int_formulaco_size(p)
, 
int_formula_size: int_formula_size(p)
, 
has-value: (a)↓
, 
nat: ℕ
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uimplies: b supposing a
Lemmas referenced : 
int_formulaco-ext, 
ifthenelse_wf, 
eq_atom_wf, 
int_term_wf, 
int_formulaco_wf, 
istype-void, 
le_wf, 
has-value_wf_base, 
set_subtype_base, 
istype-int, 
int_subtype_base, 
is-exception_wf, 
has-value_wf-partial, 
nat_wf, 
set-value-type, 
int-value-type, 
int_formulaco_size_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
cut, 
Error :dependent_set_memberEquality_alt, 
introduction, 
extract_by_obid, 
hypothesis, 
sqequalRule, 
Error :dependent_pairEquality_alt, 
tokenEquality, 
hypothesisEquality, 
Error :inhabitedIsType, 
Error :universeIsType, 
thin, 
instantiate, 
sqequalHypSubstitution, 
isectElimination, 
universeEquality, 
productEquality, 
voidEquality, 
applyEquality, 
productElimination, 
natural_numberEquality, 
independent_pairFormation, 
Error :lambdaFormation_alt, 
divergentSqle, 
sqleReflexivity, 
intEquality, 
Error :lambdaEquality_alt, 
independent_isectElimination, 
because_Cache, 
Error :equalityIsType1, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
independent_functionElimination
Latex:
\mforall{}[left,right:int\_term()].    ((left  "<"  right)  \mmember{}  int\_formula())
Date html generated:
2019_06_20-PM-00_46_07
Last ObjectModification:
2018_10_03-AM-00_45_41
Theory : omega
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