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Proof step 1 from proof finfrag-pis-nonempty (conclusion) (back to tree)

⊦ frag*(IOAut(Π(lstart, rstart), Π(lstep, rstep, lren, rren, lext, rext), Π(lext, rext, lren, rren)))(psl, pal) → πrs(lstep, rstep, lren, rren, psl, pal) ≠ []

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information

Proof step 2 from proof finfrag-pis-nonempty (previous step) (back to tree)

πrs(lstep, rstep, lren, rren, psl, pal) = [], frag*(IOAut(Π(lstart, rstart), Π(lstep, rstep, lren, rren, lext, rext), Π(lext, rext, lren, rren)))(psl, pal) ⊦

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel>, name:finfrag-pis-init, seq:⊦ frag* (IOAut (Π(lstart, rstart), Π(lstep, rstep, lren, rren, lext, rext), Π(lext, rext, lren, rren))) (psl, pal) → πrs(lstep, rstep, lren, rren, psl, pal) ≠ [] ∧ πrs(lstep, rstep, lren, rren, psl, pal).head = psl.head._2, subst:[lstart, pal, rstart, rext, lstep, lren, lext, rstep, rren, psl] → [lstart, pal, rstart, rext, lstep, lren, lext, rstep, rren, psl]

Additional information

Used terms: rext, psl, pal, rstep, rstart, lren, rren, lstart, lstep, lext

Proof step 3 from proof finfrag-pis-nonempty (previous step) (back to tree)

⊦ frag*(IOAut(Π(lstart, rstart), Π(lstep, rstep, lren, rren, lext, rext), Π(lext, rext, lren, rren)))(psl, pal) → πrs(lstep, rstep, lren, rren, psl, pal) ≠ [] ∧ πrs(lstep, rstep, lren, rren, psl, pal).head = psl.head._2

Lemma finfrag-pis-init

Proof Tree for finfrag-pis-nonempty (View conclusion)

The following image shows the proof tree of sequent calculus. The proved goal is at the bottom. You can click on the nodes to view additional rules. See here for details on colors in a proof tree.

the proof tree