Lean4 architect crafts workshop lvl0

• 04 August 2025
• Mathematics,
• Process book,
• Learning

:l4a_a #

matches:
  - trigger: ":l4a-a"
    replace: "pls show the pareto quests of Lean4 architect craft, being able to build Lean4 core and mathlib4 from scratch, and refactor it with clean code practices."
  - trigger: ":l4a-b"
    replace: "pls show micro actionable tools, actionable lead measures for each - lvl0" 
  - trigger: ":300"
    replace: "pls respond in ≤ 300 characters"

write a tactic
  what are the basic building blocks of writing a tactic?
  #maybe writing a tactic for 0 + n = n helps me understand the proof better

• intro, refl, assumption
• match & induction for structure
• trace, debug 🐛
• tactic monad 📦

my_tac := … 🎉 #

-- What is the dual of my_tac := …?
-- What is the dual of a proof?
  all arrows reversed, in
   ∃ f : Γ ⟶ φ
    which is an evaluation from ∈ ⟶ Ω #maybe
     so its dual is #perhaps Ω ⟶ ∈

∈ ⟶ Ω
Ωᵒᵖ ⟶ ∈ᵒᵖ
∃ f : Γ ⟶ φ
∀ g : φᵒᵖ ⟶ Γᵒᵖ
*presheaf ⇄ copresheaf *

F : C^op → Set (contravariant)
G : C → Set (covariant)

🤖🌿 Duality flips variance & arrow direction 🔄✨

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