Nuprl Lemma : iota_wf
∀[I:Cname List]. ∀[x:Cname]. (iota(x) ∈ name-morph(I;[x / I]))
Proof
Definitions occuring in Statement :
iota: iota(x),
name-morph: name-morph(I;J),
coordinate_name: Cname,
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iota: iota(x),
name-morph: name-morph(I;J),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
sq_type: SQType(T),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
coordinate_name_wf,
list_wf,
nameset_subtype,
cons_wf,
l_subset_right_cons_trivial,
nameset_subtype_extd-nameset,
nameset_wf,
assert_wf,
isname_wf,
equal_wf,
extd-nameset_wf,
extd-nameset_subtype,
subtype_base_sq,
extd-nameset_subtype_base,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
dependent_set_memberEquality,
lambdaEquality,
applyEquality,
independent_isectElimination,
dependent_functionElimination,
lambdaFormation,
instantiate,
cumulativity,
independent_functionElimination,
functionEquality,
functionExtensionality
Latex:
\mforall{}[I:Cname List]. \mforall{}[x:Cname]. (iota(x) \mmember{} name-morph(I;[x / I]))
Date html generated:
2017_10_05-AM-10_06_40
Last ObjectModification:
2017_07_28-AM-11_16_25
Theory : cubical!sets
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