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1. Institutions with Proofs<br />

σ : Σ → Σ ′ Sig-morphism in an institution (Sig, Sen, Mod, |=)<br />

e.g., Σ = Monoid, Σ ′ = Group, σ inclusion<br />

|Mod(Σ)| |Mod(Σ ′ |Mod(σ)|<br />

)|<br />

|=Σ<br />

|=Σ ′<br />

Sen(Σ) Sen(Σ ′ Sen(σ)<br />

)<br />

trueΣ<br />

trueΣ ′<br />

|Pf (Σ)| |Pf (Σ ′ |Pf (σ)|<br />

)|<br />

22

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