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Proof step 1 from proof Eq-P (conclusion) (back to tree)

⊦ hP0 = hP1 ↔ (∀ hP, h. ((hP0 * hP))(h) ↔ ((hP1 * hP))(h))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
hP0 ≠ hP1, ∀ hP, h. ((hP0 * hP))(h) ↔ ((hP1 * hP))(h) ⊦

Rule argument

Additional information

Proof step 2 from proof Eq-P (previous step) (back to tree)

hP0 ≠ hP1, ∀ hP, h. ((hP0 * hP))(h) ↔ ((hP1 * hP))(h) ⊦

User applied rule expand left

And obtained the following new goals

Proof step 3:
¬(hP0(h) ↔ hP1(h)), ∀ hP, h. ((hP0 * hP))(h) ↔ ((hP1 * hP))(h) ⊦

Rule argument

pos: left 1

Additional information

Proof step 3 from proof Eq-P (previous step) (back to tree)

¬(hP0(h) ↔ hP1(h)), ∀ hP, h. ((hP0 * hP))(h) ↔ ((hP1 * hP))(h) ⊦

User applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: emp, h abort: F discard: F computed: F

Additional information

Used simplifier rules: emp-sep: ⊦ emp * hP = hP; sep-ass: ⊦ (hP0 * hP1) * hP2 = hP0 * hP1 * hP2; sep-com: ⊦ hP0 * hP1 = hP1 * hP0; Used terms: emp, h

Proof Tree for Eq-P (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.