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Proof step 1 from proof val-irref (conclusion) (back to tree)

⊦ ¬ str1 < str1

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information

Proof step 2 from proof val-irref (previous step) (back to tree)

str1 < str1 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Proof step 3 from proof val-irref (previous step) (back to tree)

str1 < str1 ⊦

User applied rule structural induction

And obtained the following new goals

Rule argument

indvar: str1

Additional information

Used simplifier rules: string freely generated by "", +;;

Proof step 4 from proof val-irref (previous step) (back to tree)

char + str < char + str, ¬ str < str ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ a + x = a ' + x; (s)

Proof step 5 from proof val-irref (previous step) (back to tree)

char ' + str < char ' + str, ¬ str < str ⊦

User applied rule apply rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel>, name:Less-rec, seq:⊦ char1 ' + str1 < char2 ' + str2 ↔ char1 < char2 ∨ char1 = char2 ∧ str1 < str2, subst:[str2, char2, str1, char1] → [str, char, str, char], <all paths>

Additional information

Used simplifier rules: Char-irref: ⊦ ¬ char < char; Used terms: str, char, str, char

Proof step 6 from proof val-irref (previous step) (back to tree)

⊦ char1 ' + str1 < char2 ' + str2 ↔ char1 < char2 ∨ char1 = char2 ∧ str1 < str2

Lemma Less-rec

Proof Tree for val-irref (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