pith. machine review for the scientific record. sign in
theorem proved term proof

superconducting_gap_positive

show as:
view Lean formalization →

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

generate prose now

formal statement (Lean)

 114theorem superconducting_gap_positive (T T_c : ℝ) (hTc_pos : 0 < T_c)
 115    (hT_pos : 0 ≤ T) (hT_lt : T < T_c) :
 116    superconducting_gap T T_c hTc_pos > 0 := by

proof body

Term-mode proof.

 117  unfold superconducting_gap
 118  simp [hT_lt]
 119  apply mul_pos rs_coherence_quantum_pos
 120  rw [sub_pos, div_lt_one hTc_pos]
 121  exact hT_lt
 122
 123/-- **THEOREM EN-002.8**: The gap vanishes at and above T_c. -/

used by (2)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (9)

Lean names referenced from this declaration's body.