Nuprl Lemma : int_seg_wf
∀[m,n:ℤ]. ({m..n-} ∈ Type)
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
not_wf,
less_than'_wf,
equal-wf-base,
int_subtype_base,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
setEquality,
intEquality,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
axiomEquality,
Error :inhabitedIsType,
isect_memberEquality,
Error :universeIsType
Latex:
\mforall{}[m,n:\mBbbZ{}]. (\{m..n\msupminus{}\} \mmember{} Type)
Date html generated:
2019_06_20-AM-11_23_43
Last ObjectModification:
2018_09_26-AM-10_58_16
Theory : arithmetic
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