Nuprl Lemma : int_seg_subtype_nat
∀[a,b:ℤ]. {a..b-} ⊆r ℕ supposing 0 ≤ a
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
le: A ≤ B,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
int_seg: {i..j-},
nat: ℕ,
so_lambda: λ2x.t[x],
lelt: i ≤ j < k,
so_apply: x[s],
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
le: A ≤ B,
guard: {T}
Lemmas referenced :
subtype_rel_sets,
and_wf,
le_wf,
less_than_wf,
le_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
because_Cache,
lambdaEquality,
hypothesisEquality,
hypothesis,
natural_numberEquality,
independent_isectElimination,
setElimination,
rename,
setEquality,
lambdaFormation,
productElimination,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[a,b:\mBbbZ{}]. \{a..b\msupminus{}\} \msubseteq{}r \mBbbN{} supposing 0 \mleq{} a
Date html generated:
2016_05_13-PM-03_33_14
Last ObjectModification:
2015_12_26-AM-09_44_52
Theory : arithmetic
Home
Index