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Single Idea 13616

[filed under theme 5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions ]

Full Idea

Use of the Deduction Theorem greatly simplifies the search for proof (or more strictly, the task of showing that there is a proof).

Gist of Idea

The Deduction Theorem greatly simplifies the search for proof

Source

David Bostock (Intermediate Logic [1997], 5.3)

Book Ref

Bostock,David: 'Intermediate Logic' [OUP 1997], p.206

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A Reaction

See 13615 for details of the Deduction Theorem. Bostock is referring to axiomatic proof, where it can be quite hard to decide which axioms are relevant. The Deduction Theorem enables the making of assumptions.

Related Idea

Idea 13615 'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock]

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The 7 ideas with the same theme [proofs which add assumptions to axioms and rules]:

13616

The Deduction Theorem greatly simplifies the search for proof [Bostock]

13615

'Conditonalised' inferences point to the Deduction Theorem: If Γ,φ|-ψ then Γ|-φ→ψ [Bostock]

13620

Proof by Assumptions can always be reduced to Proof by Axioms, using the Deduction Theorem [Bostock]

13621

The Deduction Theorem and Reductio can 'discharge' assumptions - they aren't needed for the new truth [Bostock]

13690

Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms [Sider]

13691

Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step' [Sider]

10703

Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]