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theorem proved tactic proof

base_shift_denominator_forced

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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`. -/

depends on (16)

Lean names referenced from this declaration's body.