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Proof step 3 from proof wand-dual (previous step)

⊦ ((P0 -⊗ P1))(H) ↔ ¬ ((P0 -* ¬ P1))(H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ((P0 -⊗ P1))(H) ↔ (∃ H0, H1. H0 ⊥ H ∧ H1 = H0 ∪ H ∧ P0(H0) ∧ P1(H1))
Proof step 5:
⊦ (∃ H0, H1. H0 ⊥ H ∧ H1 = H0 ∪ H ∧ P0(H0) ∧ P1(H1)) ↔ ¬ ((P0 -* ¬ P1))(H)

Rule argument

spec: <toplevel> name: septract seq: ⊦ ((P0 -⊗ P1))(H) ↔ (∃ H0, H1. H0 ⊥ H ∧ H1 = H0 ∪ H ∧ P0(H0) ∧ P1(H1)) subst: [H, P1, P0] → [H, P1, P0] flags: <all paths>

Additional information

Used terms: H, P1, P0