Nuprl Lemma : int_lower_properties
∀[i:ℤ]. ∀[j:{...i}]. (j ≤ i)
Proof
Definitions occuring in Statement :
int_lower: {...i},
uall: ∀[x:A]. B[x],
le: A ≤ B,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_lower: {...i},
implies: P ⇒ Q,
all: ∀x:A. B[x],
sq_stable: SqStable(P),
squash: ↓T,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False,
prop: ℙ
Lemmas referenced :
int_lower_wf,
less_than'_wf,
decidable__le,
le_wf,
sq_stable_from_decidable
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
independent_pairEquality,
lambdaEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
intEquality
Latex:
\mforall{}[i:\mBbbZ{}]. \mforall{}[j:\{...i\}]. (j \mleq{} i)
Date html generated:
2016_05_13-PM-03_32_41
Last ObjectModification:
2016_01_14-PM-06_40_52
Theory : arithmetic
Home
Index