Nuprl Lemma : s-comp-nc-1
∀[I:fset(ℕ)]. ∀[i:ℕ]. s ⋅ (i1) = 1 ∈ I ⟶ I supposing ¬i ∈ I
Proof
Definitions occuring in Statement :
nc-1: (i1),
nc-s: s,
add-name: I+i,
nh-comp: g ⋅ f,
nh-id: 1,
names-hom: I ⟶ J,
fset-member: a ∈ s,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
fset_wf,
strong-subtype-self,
le_wf,
strong-subtype-set3,
strong-subtype-deq-subtype,
int-deq_wf,
nat_wf,
fset-member_wf,
not_wf,
dM1_wf,
s-comp-nc-p,
nc-1-as-nc-p
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
because_Cache,
independent_isectElimination,
applyEquality,
intEquality,
lambdaEquality,
natural_numberEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i:\mBbbN{}]. s \mcdot{} (i1) = 1 supposing \mneg{}i \mmember{} I
Date html generated:
2016_05_18-PM-00_01_22
Last ObjectModification:
2016_02_05-PM-00_51_54
Theory : cubical!type!theory
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