Nuprl Lemma : int_upper_subtype_int_upper
∀[n,m:ℤ]. {n...} ⊆r {m...} supposing m ≤ n
Proof
Definitions occuring in Statement :
int_upper: {i...},
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
le: A ≤ B,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
le: A ≤ B,
and: P ∧ Q,
guard: {T}
Lemmas referenced :
subtype_rel_sets,
le_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,
independent_isectElimination,
setElimination,
rename,
setEquality,
lambdaFormation,
productElimination,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n,m:\mBbbZ{}]. \{n...\} \msubseteq{}r \{m...\} supposing m \mleq{} n
Date html generated:
2016_05_13-PM-03_33_03
Last ObjectModification:
2015_12_26-AM-09_44_54
Theory : arithmetic
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