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Proof step 1 from proof strengthen-right (conclusion) (back to tree)

⊦ hP ⊆ hQ0 * hQ1 → hP ⊆ hQ0 * true

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information

Proof step 2 from proof strengthen-right (previous step) (back to tree)

hP ⊆ hQ0 * hQ1, ¬ hP ⊆ hQ0 * true ⊦

User applied rule apply rewrite lemma

And obtained the following new goals

Rule argument

spec: heap-sep, name:Imp, seq: ⊦ hP0 ⊆ hP1 ↔ (∀ h. hP0(h) → hP1(h)), subst:[hP0, hP1] → [hP, hQ0 * true], <all paths>

Additional information

Used simplifier rules: Imp1: ⊦ hP0 ⊆ hP1 ∧ hP0(h) → hP1(h); (forward) from specification heap-sep ⊦ ((hP0 * hP))(h) → ((true * hP))(h); (s) sep-ass: ⊦ (hP0 * hP1) * hP2 = hP0 * hP1 * hP2; from specification heap-sep sep-com: ⊦ hP0 * hP1 = hP1 * hP0; from specification heap-sep Used terms: hP, hQ0 * true

Proof step 3 from proof strengthen-right (previous step) (back to tree)

⊦ hP0 ⊆ hP1 ↔ (∀ h. hP0(h) → hP1(h))

A spec-lemma

Proof Tree for strengthen-right (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