Nuprl Lemma : closed-cubical-type-cumulativity
{ * ⊢ _} ⊆r { * ⊢' _}
Proof
Definitions occuring in Statement :
closed-cubical-type: { * ⊢ _},
subtype_rel: A ⊆r B
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
member: t ∈ T,
closed-cubical-type: { * ⊢ _},
and: P ∧ Q,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
all: ∀x:A. B[x]
Lemmas referenced :
fset_wf,
nat_wf,
names-hom_wf,
nh-id_wf,
nh-comp_wf,
closed-cubical-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality_alt,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
productElimination,
dependent_set_memberEquality_alt,
dependent_pairEquality_alt,
functionExtensionality,
cumulativity,
applyEquality,
hypothesisEquality,
introduction,
extract_by_obid,
isectElimination,
hypothesis,
functionIsType,
universeIsType,
inhabitedIsType,
independent_pairFormation,
sqequalRule,
productIsType,
equalityIstype,
because_Cache
Latex:
\{ * \mvdash{} \_\} \msubseteq{}r \{ * \mvdash{}' \_\}
Date html generated:
2020_05_20-PM-01_50_37
Last ObjectModification:
2020_03_20-AM-10_56_14
Theory : cubical!type!theory
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