Nuprl Lemma : in-context-dom_wf
∀[ctxt:CubicalContext]. ∀[v:varname()]. (in-context-dom(ctxt;v) ∈ ℙ)
Proof
Definitions occuring in Statement :
in-context-dom: in-context-dom(ctxt;v),
cubical_context: CubicalContext,
varname: varname(),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
in-context-dom: in-context-dom(ctxt;v),
spreadn: spread3,
cubical_context: CubicalContext
Lemmas referenced :
l_member_wf,
varname_wf,
cubical_context_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
extract_by_obid,
isectElimination,
hypothesis,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[ctxt:CubicalContext]. \mforall{}[v:varname()]. (in-context-dom(ctxt;v) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-PM-08_02_21
Last ObjectModification:
2020_02_25-PM-03_42_17
Theory : cubical!type!theory
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