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CompPoly.ToMathlib.Order.WithBot

Strict additive monotonicity on WithBot #

Mathlib's WithBot.add_lt_add_of_le_of_lt / WithBot.add_lt_add_of_lt_of_le carry ≠ ⊥ side conditions; the fully strict version below needs none of them over . Upstreaming candidate.

theorem WithBot.add_lt_add {a b c d : WithBot } (h1 : a < b) (h2 : c < d) :
a + c < b + d

Strict monotonicity of + on WithBot: a < b → c < d → a + c < b + d.