theorem
proved
tactic proof
base_shift_denominator_forced
show as:
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formal statement (Lean)
300theorem base_shift_denominator_forced
301 {k : ℕ} (hk : 0 < k)
302 (h : base_shift = 2 * (W : ℝ) +
303 ((((W + E_total : ℚ) / (k * E_passive)) : ℚ) : ℝ)) :
304 k = 4 := by
proof body
Tactic-mode proof.
305 have hcanon : base_shift = 2 * (W : ℝ) + (ledger_fraction : ℝ) := by
306 simp [base_shift]
307 have hfracR :
308 ((((W + E_total : ℚ) / (k * E_passive)) : ℚ) : ℝ) = (ledger_fraction : ℝ) := by
309 linarith [h, hcanon]
310 have hfracQ : ((W + E_total : ℚ) / (k * E_passive)) = ledger_fraction := by
311 exact_mod_cast hfracR
312 exact ledger_fraction_denominator_forced hk hfracQ
313
314/-- Positivity-free packaged denominator forcing for `base_shift`:
315 with canonical `2W` term fixed, matching
316 `2W + (W+E)/(kE_p)` still forces `k = 4` without explicit `k > 0`. -/