Nuprl Lemma : add-name_wf
∀[I:fset(ℕ)]. ∀[i:ℕ]. (I+i ∈ fset(ℕ))
Proof
Definitions occuring in Statement :
add-name: I+i,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
add-name: I+i,
names-deq: NamesDeq,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
fset-add_wf,
nat_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
fset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
intEquality,
independent_isectElimination,
because_Cache,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i:\mBbbN{}]. (I+i \mmember{} fset(\mBbbN{}))
Date html generated:
2016_05_18-AM-11_59_58
Last ObjectModification:
2015_12_28-PM-03_06_47
Theory : cubical!type!theory
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