Nuprl Lemma : cubical_context_val_wf
∀[ctxt:CubicalContext]. ∀[v:varname()].
cubical_context_val(ctxt;v) ∈ cttTerm(fst(ctxt)) supposing in-context-dom(ctxt;v)
Proof
Definitions occuring in Statement :
cubical_context_val: cubical_context_val(ctxt;v),
in-context-dom: in-context-dom(ctxt;v),
cubical_context: CubicalContext,
ctt-term-meaning: cttTerm(X),
varname: varname(),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pi1: fst(t),
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
cubical_context_val: cubical_context_val(ctxt;v),
cubical_context: CubicalContext,
spreadn: spread3,
in-context-dom: in-context-dom(ctxt;v),
pi1: fst(t),
prop: ℙ
Lemmas referenced :
l_member_wf,
varname_wf,
in-context-dom_wf,
cubical_context_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
applyEquality,
hypothesisEquality,
dependent_set_memberEquality_alt,
hypothesis,
universeIsType,
extract_by_obid,
isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[ctxt:CubicalContext]. \mforall{}[v:varname()].
cubical\_context\_val(ctxt;v) \mmember{} cttTerm(fst(ctxt)) supposing in-context-dom(ctxt;v)
Date html generated:
2020_05_20-PM-08_03_01
Last ObjectModification:
2020_05_03-PM-05_52_06
Theory : cubical!type!theory
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