# Concept derivation guides

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Concept guide



## [Proof term: reading λh. ⟨snd h, fst h⟩ part by part as a proof term for P∧Q→Q∧P](/en/derivations/derivation-mko-lean-proof-term-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-lean-proof-term)

In an explicit synthetic small propositional type system ST (matching MKO assumption a2), with distinct propositional atoms P and Q: explain part by part what each piece of the term t=λh:P∧Q. ⟨snd h, fst h⟩ establishes and what type it has, derive the judgment ⊢ t : P∧Q→Q∧P, and explain why the type of t matches the proposition S=P∧Q→Q∧P; then prove that the similar-looking t′=λh:P∧Q. ⟨fst h, snd h⟩ is not a proof term for S. Finally separate three things: a typing derivation in ST, acceptance by the Lean kernel, and a saved proof-term receipt.

Proof term

derivation-mko-lean-proof-term-01





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