Theorems · Definition · logic and foundations
Turing.Tape.nth
{Γ : Type u_1} → [inst : Inhabited Γ] → Turing.Tape Γ → ℤ → ΓThe nth function of a tape is integer-valued, with index 0 being the head, negative indexes
on the left and positive indexes on the right. (Picture a number line.)
- Defined in
- Mathlib.Computability.TuringMachine.Tape
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Inhabited
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Turing.Tapestatement and proof · cited by 50
- Turing.ListBlank.nthproof · cited by 17
- Turing.Tape.headproof · cited by 17
- Turing.Tape.leftproof · cited by 6
- Turing.Tape.rightproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- Turing.Tape.mk'_nth_natstatement · cited by 4
- Turing.Tape.move_right_n_headstatement and proof · cited by 4
- Turing.TM2to1.tr_respects_aux₂proof · cited by 1
- Turing.Tape.move_left_nthstatement and proof · cited by 1
- Turing.Tape.move_right_nthstatement and proof · cited by 1
- Turing.Tape.right₀_nthstatement · cited by 1
- Turing.Tape.nth_zerostatement · cited by 0
- Turing.Tape.write_nthstatement and proof · cited by 0