Nuprl Lemma : degeneracy-map_wf
∀[I,J:Cname List]. ∀[f:nameset(I) ⟶ nameset(J)].
degeneracy-map(f) ∈ name-morph(I;J) supposing Inj(nameset(I);nameset(J);f)
Proof
Definitions occuring in Statement :
degeneracy-map: degeneracy-map(f),
name-morph: name-morph(I;J),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
inject: Inj(A;B;f),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
name-morph: name-morph(I;J),
degeneracy-map: degeneracy-map(f),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
inject: Inj(A;B;f),
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
nameset_subtype_extd-nameset,
nameset_wf,
equal_wf,
extd-nameset_wf,
assert_wf,
all_wf,
isname_wf,
inject_wf,
list_wf,
coordinate_name_wf,
subtype_base_sq,
extd-nameset_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
functionExtensionality,
applyEquality,
hypothesisEquality,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaFormation,
because_Cache,
lambdaEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
dependent_functionElimination,
independent_functionElimination,
instantiate,
cumulativity,
independent_isectElimination
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:nameset(I) {}\mrightarrow{} nameset(J)].
degeneracy-map(f) \mmember{} name-morph(I;J) supposing Inj(nameset(I);nameset(J);f)
Date html generated:
2017_10_05-AM-10_06_34
Last ObjectModification:
2017_07_28-AM-11_16_24
Theory : cubical!sets
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