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Proof step 1 from proof lastdiv-rew (conclusion) (back to tree)

⊦ x = [] ↔ ¬(∃ y, a. x = y + a ')

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
x ≠ [] ⊦ ∃ y, a. x = y + a '

Rule argument

Additional information

Used simplifier rules: e-02: ⊦ x + a ' ≠ []; a: ⊦ (x + y) + z = x + y + z;

Proof step 2 from proof lastdiv-rew (previous step) (back to tree)

x ≠ [] ⊦ ∃ y, a. x = y + a '

User applied rule apply lemma

And obtained the following new goals

Proof step 3:
⊦ x ≠ [] → (∃ y, a. x = y + a ')

Rule argument

spec: <toplevel>, name:lastdiv, seq: ⊦ x ≠ [] → (∃ y, a. x = y + a '), subst:[x] → [x]

Additional information

Used terms: x

Proof step 3 from proof lastdiv-rew (previous step) (back to tree)

⊦ x ≠ [] → (∃ y, a. x = y + a ')

Lemma lastdiv

Proof Tree for lastdiv-rew (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.