theorem
proved
tactic proof
base_shift_weight_split_forced
show as:
view Lean formalization →
formal statement (Lean)
366theorem base_shift_weight_split_forced
367 {a b : ℚ}
368 (hsum : a + b = 2)
369 (h : base_shift = 2 * (W : ℝ) +
370 ((((a * (W : ℚ) + b * (E_total : ℚ)) / (4 * E_passive)) : ℚ) : ℝ)) :
371 a = 1 ∧ b = 1 := by
proof body
Tactic-mode proof.
372 have hcanon : base_shift = 2 * (W : ℝ) + (ledger_fraction : ℝ) := by
373 simp [base_shift]
374 have hfracR :
375 ((((a * (W : ℚ) + b * (E_total : ℚ)) / (4 * E_passive)) : ℚ) : ℝ) = (ledger_fraction : ℝ) := by
376 linarith [h, hcanon]
377 have hfracQ : ((a * (W : ℚ) + b * (E_total : ℚ)) / (4 * E_passive)) = ledger_fraction := by
378 exact_mod_cast hfracR
379 exact ledger_fraction_weight_split_forced hsum hfracQ
380
381/-- Packaged `base_shift` closure for integer numerator/denominator perturbations:
382 under passive-edge band `n ≤ E_p`, matching
383 `2W + ((W+E)+n)/(kE_p)` forces `k = 4` and `n = 0`. -/