Nuprl Lemma : csm-equal
∀[A,B:CubicalSet]. ∀[f:A ⟶ B]. ∀[g:I:(Cname List) ⟶ A(I) ⟶ B(I)].
f = g ∈ A ⟶ B supposing f = g ∈ (I:(Cname List) ⟶ A(I) ⟶ B(I))
Proof
Definitions occuring in Statement :
I-cube: X(I),
cube-set-map: A ⟶ B,
cubical-set: CubicalSet,
coordinate_name: Cname,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
cube-set-map: A ⟶ B,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
type-cat: TypeCat,
cat-arrow: cat-arrow(C),
name-cat: NameCat,
cat-ob: cat-ob(C),
pi1: fst(t),
pi2: snd(t),
I-cube: X(I),
cubical-set: CubicalSet,
nat-trans: nat-trans(C;D;F;G),
functor-ob: functor-ob(F),
cat-comp: cat-comp(C)
Lemmas referenced :
list_wf,
coordinate_name_wf,
I-cube_wf,
cube-set-map_wf,
cubical-set_wf,
cubical-set-is-functor,
nat-trans-equal,
name-cat_wf,
type-cat_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
functionEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
productElimination,
instantiate,
applyEquality,
sqequalRule,
independent_isectElimination,
setElimination,
rename
Latex:
\mforall{}[A,B:CubicalSet]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[g:I:(Cname List) {}\mrightarrow{} A(I) {}\mrightarrow{} B(I)]. f = g supposing f = g
Date html generated:
2016_06_16-PM-05_36_14
Last ObjectModification:
2015_12_28-PM-04_37_37
Theory : cubical!sets
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