Nuprl Lemma : decode-equivTerm
∀[G:j⊢]. ∀[A,B:{G ⊢ _:c𝕌}]. (decode(equivTerm(G;A;B)) = Equiv(decode(A);decode(B)) ∈ {G ⊢ _})
Proof
Definitions occuring in Statement :
equivTerm: equivTerm(G;A;B),
universe-decode: decode(t),
cubical-universe: c𝕌,
cubical-equiv: Equiv(T;A),
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
equivTerm: equivTerm(G;A;B),
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
universe-decode-encode,
cubical-equiv_wf,
universe-decode_wf,
equiv-comp_wf,
universe-comp-op_wf,
istype-cubical-universe-term,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
universeIsType,
instantiate
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A,B:\{G \mvdash{} \_:c\mBbbU{}\}]. (decode(equivTerm(G;A;B)) = Equiv(decode(A);decode(B)))
Date html generated:
2020_05_20-PM-07_34_06
Last ObjectModification:
2020_04_30-AM-00_11_49
Theory : cubical!type!theory
Home
Index