Nuprl Lemma : nc-0-s-commute
∀[I:fset(ℕ)]. ∀[i,j:ℕ]. ((i0) ⋅ s = s ⋅ (i0) ∈ I+j ⟶ I+i)
Proof
Definitions occuring in Statement :
nc-0: (i0),
nc-s: s,
add-name: I+i,
nh-comp: g ⋅ f,
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
fset_wf,
nat_wf,
nc-0-as-nc-p,
nc-p-s-commute
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
sqequalRule
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i,j:\mBbbN{}]. ((i0) \mcdot{} s = s \mcdot{} (i0))
Date html generated:
2016_05_18-PM-00_05_18
Last ObjectModification:
2016_02_08-PM-03_10_38
Theory : cubical!type!theory
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