Nuprl Lemma : int_seg_subtype_upper
∀[m1,n1,m2:ℤ]. {m1..n1-} ⊆r {m2...} supposing m2 ≤ m1
Proof
Definitions occuring in Statement :
int_upper: {i...},
int_seg: {i..j-},
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_seg: {i..j-},
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
lelt: i ≤ j < k,
and: P ∧ Q,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
le: A ≤ B,
guard: {T}
Lemmas referenced :
subtype_rel_sets,
lelt_wf,
le_wf,
le_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_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{}[m1,n1,m2:\mBbbZ{}]. \{m1..n1\msupminus{}\} \msubseteq{}r \{m2...\} supposing m2 \mleq{} m1
Date html generated:
2018_05_21-PM-00_03_57
Last ObjectModification:
2018_05_19-AM-07_10_32
Theory : int_1
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