relrank_eq_rank_of_le — Mathlib

English

Relational equality tying inf-relations to nat-relations: relfinrank_mul_relfinrank_eq_inf_relfinrank.

Русский

Связь между инф- и нат-рангами через равенство: relfinrank_mul_relfinrank_eq_inf_relfinrank.

LaTeX

$$$\\text{If } B \\le C,\\; \\operatorname{relfinrank}(A,B) \\cdot \\operatorname{relfinrank}(B,C) = (A \\cap B).\\operatorname{relfinrank}(C).$$$

Lean4

/-- If `A ≤ B`, then `IntermediateField.relrank A B` is `[B : A]` -/
theorem relrank_eq_rank_of_le (h : A ≤ B) : relrank A B = Module.rank A (extendScalars h) :=
  Subfield.relrank_eq_rank_of_le h

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