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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