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Step * of Lemma callbyvalueall-seq-extend0-2

∀[F,G,L:Top]. ∀[m:ℕ+].
  (callbyvalueall-seq(L;λx.x;mk_lambdas(λout.let x ⟵ F[out]
                                             in G[x];m - 1);0;m) ~ callbyvalueall-seq(λn.if (n =z m)
                                                                                         then mk_lambdas(λx.F[x];m - 1)
                                                                                         else L n
                                                                                         fi ;λx.x;mk_lambdas(λx.G[x];m)
                                                                                      ;0;m + 1))
BY
{ ((UnivCD THENA Auto)
   THEN (InstLemma `callbyvalueall-seq-extend-2` [⌜F⌝;⌜G⌝;⌜L⌝;⌜λx.x⌝;⌜m⌝;⌜0⌝]⋅ THENA Auto)
   THEN RepUR ``mk_applies`` (-1)
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[F,G,L:Top].  \mforall{}[m:\mBbbN{}\msupplus{}].
    (callbyvalueall-seq(L;\mlambda{}x.x;mk\_lambdas(\mlambda{}out.let  x  \mleftarrow{}{}  F[out]
                                                                                          in  G[x];m  -  1);0;m) 
    \msim{}  callbyvalueall-seq(\mlambda{}n.if  (n  =\msubz{}  m)  then  mk\_lambdas(\mlambda{}x.F[x];m  -  1)  else  L  n  fi  ;\mlambda{}x.x
                                              ;mk\_lambdas(\mlambda{}x.G[x];m);0;m  +  1))


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  (InstLemma  `callbyvalueall-seq-extend-2`  [\mkleeneopen{}F\mkleeneclose{};\mkleeneopen{}G\mkleeneclose{};\mkleeneopen{}L\mkleeneclose{};\mkleeneopen{}\mlambda{}x.x\mkleeneclose{};\mkleeneopen{}m\mkleeneclose{};\mkleeneopen{}0\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  RepUR  ``mk\_applies``  (-1)
  THEN  Auto)

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