Nuprl Lemma : s-comp-nc-1-new
∀[I:fset(ℕ)]. (s ⋅ (new-name(I)1) = 1 ∈ I ⟶ I)
Proof
Definitions occuring in Statement :
nc-1: (i1),
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-1,
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)1) = 1)
Date html generated:
2020_05_20-PM-01_36_39
Last ObjectModification:
2020_01_06-AM-11_10_10
Theory : cubical!type!theory
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