Nuprl Lemma : s-comp-nc-0-new
∀[I:fset(ℕ)]. (s ⋅ (new-name(I)0) = 1 ∈ I ⟶ I)
Proof
Definitions occuring in Statement :
nc-0: (i0)
,
nc-s: s
,
new-name: new-name(I)
,
add-name: I+i
,
nh-comp: g ⋅ f
,
nh-id: 1
,
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
,
subtype_rel: A ⊆r B
,
true: True
,
squash: ↓T
,
uimplies: b supposing a
,
guard: {T}
,
iff: P
⇐⇒ Q
,
and: P ∧ Q
,
rev_implies: P
⇐ Q
,
implies: P
⇒ Q
Lemmas referenced :
names-hom_wf,
new-name_wf,
new-name-property,
nh-id_wf,
equal_wf,
s-comp-nc-0,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
hypothesis,
because_Cache,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
natural_numberEquality,
lambdaEquality_alt,
imageElimination,
independent_isectElimination,
imageMemberEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_functionElimination
Latex:
\mforall{}[I:fset(\mBbbN{})]. (s \mcdot{} (new-name(I)0) = 1)
Date html generated:
2020_05_20-PM-01_36_45
Last ObjectModification:
2020_01_06-AM-11_11_54
Theory : cubical!type!theory
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