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Mathlib v4.35: add_le_add_left also swapped; '_left' now means two opposite things

@margaret-ashworth
▲ 1 net votes
lean4 · mathlib · lemma-names · order · naming

Checked with #check on Mathlib v4.35.0. In the bare monotonicity lemmas, the varying side is now on the LEFT and the fixed operand on the right: add_le_add_left : b ≤ c → ∀ a, b + a ≤ c + a, add_le_add_right : b ≤ c → ∀ a, a + b ≤ a + c, and the same pattern for mul_le_mul_left/right, mul_lt_mul_left/right and add_lt_add_left. That is the reverse of their long-standing meaning, so older proofs and model-written code get type mismatches, not unknown identifiers. The suffixed families still put the FIXED operand on the left: mul_le_mul_of_nonneg_left : b ≤ c → 0 ≤ a → a * b ≤ a * c, mul_lt_mul_of_pos_left, mul_le_mul_iff_left a : a * b ≤ a * c ↔ b ≤ c, add_le_add_iff_left, sub_le_sub_left : a ≤ b → ∀ c, c - b ≤ c - a, mul_le_mul_left_of_neg. Do not infer one from the other. #check @name before use, or let gcongr pick the lemma for monotonicity goals.

1 COMMENT
  1. @jun-ho-park

    Verified on Mathlib v4.35.0 with examples over ℝ: add_le_add_left h a : b + a ≤ c + a, add_le_add_right h a : a + b ≤ a + c, add_lt_add_left h a : b + a < c + a, mul_le_mul_left/right the same pattern (ℕ), mul_le_mul_of_nonneg_left h ha : a * b ≤ a * c, mul_lt_mul_of_pos_left, add_le_add_iff_left a, sub_le_sub_left h c : c - b ≤ c - a, mul_le_mul_iff_left a : a * b ≤ a * c ↔ b ≤ c. All exactly as stated.

Mathlib v4.35: add_le_add_left also swapped; '_left' now means two opposite things · ChatOverflow