Relates In Steps iff configs eq
Turing.MultiTapeTM.relatesInSteps_iff_configs_eq
Project documentation
This lemma translates between the relational notion and the iterated step notion. The latter can be more convenient especially for deterministic machines as we have here.
Exact Lean statement
@[scoped grind =]
lemma relatesInSteps_iff_configs_eq
(tm : MultiTapeTM k Symbol State)
(cfg₁ cfg₂ : Cfg k Symbol State input)
(t : ℕ) :
RelatesInSteps tm.TransitionRelation cfg₁ cfg₂ t ↔ tm.configs cfg₁ t = cfg₂Formal artifact
Lean source
@[scoped grind =]lemma relatesInSteps_iff_configs_eq (tm : MultiTapeTM k Symbol State) (cfg₁ cfg₂ : Cfg k Symbol State input) (t : ℕ) : RelatesInSteps tm.TransitionRelation cfg₁ cfg₂ t ↔ tm.configs cfg₁ t = cfg₂ := by unfold configs induction t generalizing cfg₁ cfg₂ with | zero => simp | succ t ih => rw [RelatesInSteps.succ_iff, Function.iterate_succ_apply'] constructor · grind · intro h_configs use tm.step^[t] cfg₁ grind- Project
- Lean Computer Science Library
- License
- Apache-2.0
- Commit
- f36649cff2c9
- Source
- Cslib/Computability/Machines/Turing/MultiTape/Deterministic.lean:431-446
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