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Step * of Lemma name-path-endpoints_wf

∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[a,b:{X ⊢ _:A}]. ∀[I:Cname List]. ∀[alpha:X(I)]. ∀[z:Cname]. ∀[omega:A(iota(z)(alpha))].
  name-path-endpoints(X;A;a;b;I;alpha;z;omega) ∈ ℙ supposing ¬(z ∈ I)
BY
{ (ProveWfLemma
   THEN (InstLemma `cubical-type-ap-morph_wf` [⌜X⌝;⌜A⌝;⌜[z / I]⌝;⌜I⌝;⌜(z:=0)⌝;⌜iota(z)(alpha)⌝;⌜omega⌝]⋅ THENA Auto)
   THEN (InstLemma `cubical-type-ap-morph_wf` [⌜X⌝;⌜A⌝;⌜[z / I]⌝;⌜I⌝;⌜(z:=1)⌝;⌜iota(z)(alpha)⌝;⌜omega⌝]⋅ THENA Auto)
   THEN InferEqualType
   THEN Auto
   THEN (InstLemma `iota-identity` [⌜I⌝;⌜z⌝]⋅ THENA Auto)
   THEN RWO "-1" 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[X:CubicalSet].  \mforall{}[A:\{X  \mvdash{}  \_\}].  \mforall{}[a,b:\{X  \mvdash{}  \_:A\}].  \mforall{}[I:Cname  List].  \mforall{}[alpha:X(I)].  \mforall{}[z:Cname].
\mforall{}[omega:A(iota(z)(alpha))].
    name-path-endpoints(X;A;a;b;I;alpha;z;omega)  \mmember{}  \mBbbP{}  supposing  \mneg{}(z  \mmember{}  I)


By

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Latex:
(ProveWfLemma
  THEN  (InstLemma  `cubical-type-ap-morph\_wf`  [\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}[z  /  I]\mkleeneclose{};\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}(z:=0)\mkleeneclose{};\mkleeneopen{}iota(z)(alpha)\mkleeneclose{};\mkleeneopen{}omega\mkleeneclose{}
              ]\mcdot{}
              THENA  Auto
              )
  THEN  (InstLemma  `cubical-type-ap-morph\_wf`  [\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}[z  /  I]\mkleeneclose{};\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}(z:=1)\mkleeneclose{};\mkleeneopen{}iota(z)(alpha)\mkleeneclose{};\mkleeneopen{}omega\mkleeneclose{}
              ]\mcdot{}
              THENA  Auto
              )
  THEN  InferEqualType
  THEN  Auto
  THEN  (InstLemma  `iota-identity`  [\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}z\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  RWO  "-1"  0
  THEN  Auto)

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