Nuprl Lemma : extd-nameset-nil
extd-nameset([]) ⊆r ℕ2
Proof
Definitions occuring in Statement :
extd-nameset: extd-nameset(L),
nil: [],
int_seg: {i..j-},
subtype_rel: A ⊆r B,
natural_number: $n
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
member: t ∈ T,
extd-nameset: extd-nameset(L),
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
pi2: snd(t),
nameset: nameset(L),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
false: False
Lemmas referenced :
nil_member,
coordinate_name_wf,
extd-nameset_wf,
nil_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
productElimination,
thin,
unionElimination,
equalityElimination,
sqequalRule,
hypothesis,
setElimination,
rename,
lemma_by_obid,
isectElimination,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
voidElimination
Latex:
extd-nameset([]) \msubseteq{}r \mBbbN{}2
Date html generated:
2016_05_20-AM-09_29_06
Last ObjectModification:
2015_12_28-PM-04_47_48
Theory : cubical!sets
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