Nuprl Lemma : face-name-eq_wf
∀[I:Cname List]. ∀[a,b:nameset(I) × ℕ2]. (face-name-eq(a;b) ∈ 𝔹)
Proof
Definitions occuring in Statement :
face-name-eq: face-name-eq(a;b),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
int_seg: {i..j-},
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
face-name-eq: face-name-eq(a;b),
subtype_rel: A ⊆r B,
nameset: nameset(L),
coordinate_name: Cname,
int_upper: {i...},
int_seg: {i..j-}
Lemmas referenced :
product-deq_wf,
int-deq_wf,
nameset_wf,
int_seg_wf,
list_wf,
coordinate_name_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
because_Cache,
hypothesis,
productElimination,
independent_pairEquality,
setElimination,
rename,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
natural_numberEquality,
isect_memberEquality
Latex:
\mforall{}[I:Cname List]. \mforall{}[a,b:nameset(I) \mtimes{} \mBbbN{}2]. (face-name-eq(a;b) \mmember{} \mBbbB{})
Date html generated:
2016_06_16-PM-05_49_24
Last ObjectModification:
2015_12_28-PM-04_31_19
Theory : cubical!sets
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