Nuprl Lemma : int_lower_well_founded
∀n:ℤ. WellFnd{i}({...n};x,y.x > y)
Proof
Definitions occuring in Statement :
int_lower: {...i},
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
gt: i > j,
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
nat: ℕ,
so_apply: x[s1;s2],
int_lower: {...i},
prop: ℙ,
implies: P ⇒ Q,
subtract: n - m,
le: A ≤ B,
and: P ∧ Q,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
top: Top,
uiff: uiff(P;Q),
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
not: ¬A,
false: False,
decidable: Dec(P),
or: P ∨ Q,
gt: i > j,
iff: P ⇐⇒ Q,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
so_apply: x[s]
Lemmas referenced :
nat_well_founded,
inv_image_ind,
nat_wf,
less_than_wf,
int_lower_wf,
subtract_wf,
le_wf,
minus-one-mul,
add_functionality_wrt_le,
le_reflexive,
minus-one-mul-top,
istype-void,
one-mul,
add-swap,
add-commutes,
add-associates,
add-mul-special,
two-mul,
mul-distributes-right,
zero-mul,
zero-add,
not-le-2,
minus-zero,
add-zero,
omega-shadow,
mul-distributes,
mul-associates,
mul-commutes,
le-add-cancel-alt,
int_lower_properties,
decidable__le,
wellfounded_functionality_wrt_iff,
iff_weakening_uiff,
minus_mono_wrt_lt,
gt_wf,
subtype_rel_self,
minus-add,
minus-minus,
not-lt-2,
istype-int,
less-iff-le,
decidable__lt
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
Error :universeIsType,
intEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :lambdaEquality_alt,
setElimination,
rename,
because_Cache,
Error :inhabitedIsType,
hypothesisEquality,
dependent_functionElimination,
Error :dependent_set_memberEquality_alt,
natural_numberEquality,
independent_functionElimination,
productElimination,
multiplyEquality,
independent_isectElimination,
applyEquality,
Error :isect_memberEquality_alt,
voidElimination,
addEquality,
minusEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
unionElimination,
Error :isect_memberFormation_alt,
Error :functionIsType,
instantiate,
universeEquality
Latex:
\mforall{}n:\mBbbZ{}. WellFnd\{i\}(\{...n\};x,y.x > y)
Date html generated:
2019_06_20-AM-11_28_04
Last ObjectModification:
2018_10_05-PM-00_16_59
Theory : call!by!value_2
Home
Index