Nuprl Lemma : int_seg_subtype
∀[m1,n1,m2,n2:ℤ]. {m1..n1-} ⊆r {m2..n2-} supposing (m2 ≤ m1) ∧ (n1 ≤ n2)
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
le: A ≤ B,
and: P ∧ Q,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
lelt: i ≤ j < k,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
le: A ≤ B,
guard: {T}
Lemmas referenced :
subtype_rel_sets,
lelt_wf,
le_transitivity,
less_than_transitivity1,
and_wf,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
lemma_by_obid,
isectElimination,
intEquality,
because_Cache,
lambdaEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
setElimination,
rename,
setEquality,
lambdaFormation,
independent_pairFormation,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[m1,n1,m2,n2:\mBbbZ{}]. \{m1..n1\msupminus{}\} \msubseteq{}r \{m2..n2\msupminus{}\} supposing (m2 \mleq{} m1) \mwedge{} (n1 \mleq{} n2)
Date html generated:
2016_05_13-PM-04_02_00
Last ObjectModification:
2015_12_26-AM-10_56_51
Theory : int_1
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