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Theorem copy-node-prepost

⊦ copy-node-prepost(H0, H, map) ↔ (∃ H1. H0 ∪ H1 = H ∧ H0 ⊥ H1 ∧ dom map ⊆ dom H0 ∧ ran map = dom H1 ∧ closed(H0) ∧ closed(H1) ∧ inj(map))