Nuprl Lemma : glue-type-subset
∀[Gamma,A,phi,T,w,xx:Top]. (Gamma, xx ⊢ Glue [phi ⊢→ (T;w)] A ~ Gamma ⊢ Glue [phi ⊢→ (T;w)] A)
Proof
Definitions occuring in Statement :
glue-type: Glue [phi ⊢→ (T;w)] A,
context-subset: Gamma, phi,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
glue-type: Glue [phi ⊢→ (T;w)] A,
context-subset: Gamma, phi,
glue-morph: glue-morph(Gamma;A;phi;T;w;I;rho;J;f;u),
glue-cube: glue-cube(Gamma;A;phi;T;w;I;rho),
all: ∀x:A. B[x],
member: t ∈ T,
glue-equations: glue-equations(Gamma;A;phi;T;w;I;rho;t;a)
Lemmas referenced :
cube_set_restriction_pair_lemma,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
Error :memTop,
hypothesis,
because_Cache,
inhabitedIsType,
hypothesisEquality
Latex:
\mforall{}[Gamma,A,phi,T,w,xx:Top]. (Gamma, xx \mvdash{} Glue [phi \mvdash{}\mrightarrow{} (T;w)] A \msim{} Gamma \mvdash{} Glue [phi \mvdash{}\mrightarrow{} (T;w)] A)
Date html generated:
2020_05_20-PM-05_40_58
Last ObjectModification:
2020_04_21-PM-05_55_16
Theory : cubical!type!theory
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