Step from to Standard Form
Cslib.URM.Step.from_toStandardForm
Plain-language statement
Reverse step correspondence: if p.toStandardForm steps from s to s', then either: (1) p steps from s to s' (same step), or (2) s' is halted in p.toStandardForm, and p steps to a state that is also halted with the same registers (this only happens for jumps with unbounded targets).
Exact Lean statement
theorem Step.from_toStandardForm {p : Program} {s s' : State} (hstep : Step p.toStandardForm s s') :
Step p s s' ∨
(s'.isHalted p.toStandardForm ∧ ∃ s₂, Step p s s₂ ∧ s₂.isHalted p ∧ s'.regs = s₂.regs)Formal artifact
Lean source
theorem Step.from_toStandardForm {p : Program} {s s' : State} (hstep : Step p.toStandardForm s s') : Step p s s' ∨ (s'.isHalted p.toStandardForm ∧ ∃ s₂, Step p s s₂ ∧ s₂.isHalted p ∧ s'.regs = s₂.regs) := by cases hstep with | jump_eq hinstr _ => simp only [Program.getElem?_toStandardForm, Option.map_eq_some_iff] at hinstr obtain ⟨instr, _⟩ := hinstr cases instr with | J => grind [=> jump_eq] | _ => grind | _ => grind [getElem?_toStandardForm, Option.map_eq_some_iff]- Project
- Lean Computer Science Library
- License
- Apache-2.0
- Commit
- f36649cff2c9
- Source
- Cslib/Computability/URM/StandardForm.lean:156-166
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Unique minimal
Cslib.Automata.DA.FinAcc.unique_minimal
Plain-language statement
The minimal DFA M accepting the language l is unique up to unique isomorphism.
Source project: Lean Computer Science Library
Person-level attribution pending.
Buchi Family cover
Cslib.Automata.NA.Buchi.buchiFamily_cover
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Source project: Lean Computer Science Library
Person-level attribution pending.
Buchi Family saturation
Cslib.Automata.NA.Buchi.buchiFamily_saturation
Plain-language statement
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Source project: Lean Computer Science Library
Person-level attribution pending.