Nuprl Lemma : csm-same-cubical-type
∀[Gamma:j⊢]. ∀[A,B:{Gamma ⊢ _}]. ∀[H:j⊢]. ∀[s:H j⟶ Gamma]. H ⊢ (A)s = (B)s supposing Gamma ⊢ A = B
Proof
Definitions occuring in Statement :
same-cubical-type: Gamma ⊢ A = B,
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
same-cubical-type: Gamma ⊢ A = B,
and: P ∧ Q
Lemmas referenced :
csm-ap-type_wf,
cube_set_map_wf,
same-cubical-type_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
equalitySymmetry,
dependent_set_memberEquality_alt,
hypothesis,
independent_pairFormation,
equalityTransitivity,
sqequalRule,
productIsType,
equalityIstype,
inhabitedIsType,
hypothesisEquality,
applyLambdaEquality,
setElimination,
thin,
rename,
productElimination,
extract_by_obid,
isectElimination,
axiomEquality,
universeIsType,
instantiate,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A,B:\{Gamma \mvdash{} \_\}].
\mforall{}[H:j\mvdash{}]. \mforall{}[s:H j{}\mrightarrow{} Gamma]. H \mvdash{} (A)s = (B)s supposing Gamma \mvdash{} A = B
Date html generated:
2020_05_20-PM-02_59_48
Last ObjectModification:
2020_04_06-AM-10_33_03
Theory : cubical!type!theory
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