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Proof step 1 from proof projaction-rec-addR-one (conclusion) (back to tree)

⊦ rstep(rs, ra, rs0) ∧ ¬ cod(lren)(rren(ra)) → πra(lstep, rstep, lren, rren, (ls, rs) ' + (ls, rs0) ', rren(ra) ') = ra + πra(lstep, rstep, lren, rren, (ls, rs0) ', [])

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information

Proof step 2 from proof projaction-rec-addR-one (previous step) (back to tree)

πra(lstep, rstep, lren, rren, (ls, rs) ' + (ls, rs0) ', rren(ra) ') ≠ ra + πra(lstep, rstep, lren, rren, (ls, rs0) ', []), rstep(rs, ra, rs0), ¬ cod(lren)(rren(ra)) ⊦

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel>, name:projaction-rec-addR, seq:⊦ # psl = # pal ∧ rstep(rs, ra, rs0) ∧ ¬ cod(lren)(rren(ra)) → πra(lstep, rstep, lren, rren, (ls, rs) ' + (ls, rs0) ' + psl, rren(ra) ' + pal) = ra + πra(lstep, rstep, lren, rren, (ls, rs0) + psl, pal), subst:[pal, lstep, rs0, ra, ls, rs, lren, rstep, rren, psl] → [[], lstep, rs0, ra, ls, rs, lren, rstep, rren, []]; ['ls, 'ra, 'la, 'pa, 'rs] → ['ls, 'ra, 'la, 'pa, 'rs]

Additional information

Used simplifier rules: projaction-base: ⊦ πra(lstep, rstep, lren, rren, (ls, rs) ', []) = []; ⊦ # [] = 0; (s) ⊦ a + x = a ' + x; (s) ⊦ x + [] = x; (s) a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: [], rs, ra, [], rstep, lren, rren, rs0, lstep, ls

Proof step 3 from proof projaction-rec-addR-one (previous step) (back to tree)

⊦ # psl = # pal ∧ rstep(rs, ra, rs0) ∧ ¬ cod(lren)(rren(ra)) → πra(lstep, rstep, lren, rren, (ls, rs) ' + (ls, rs0) ' + psl, rren(ra) ' + pal) = ra + πra(lstep, rstep, lren, rren, (ls, rs0) + psl, pal)

Lemma projaction-rec-addR

Proof Tree for projaction-rec-addR-one (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