| {"id":"MyNat","label":"MyNat","background_color":"#B0ECA3","border_color":"green","kind":"box","dep_graph_url":"https://hanwenzhu.github.io/LeanArchitect-example/blueprint/dep_graph_document.html","dependencies":[],"nlp_text":"Natural numbers.","doc_url":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat","latex_link":"index.html#MyNat","lean_link":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat","lean_decl_name":"MyNat","kind_description":"definitions","status_from_color":"formalized","lookup_in_mathlib4v4.22.0":true,"found_in_mathlib4v4.22.0":false,"proof_status":"nlp_only"} |
| {"id":"def:nat-add","label":"nat-add","background_color":"#B0ECA3","border_color":"green","kind":"box","dep_graph_url":"https://hanwenzhu.github.io/LeanArchitect-example/blueprint/dep_graph_document.html","dependencies":["MyNat"],"nlp_text":"Natural number addition.","doc_url":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.add","latex_link":"index.html#def:nat-add","lean_link":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.add","lean_decl_name":"MyNat.add","kind_description":"definitions","status_from_color":"formalized","lookup_in_mathlib4v4.22.0":false,"found_in_mathlib4v4.22.0":false,"source_repo":"LeanArchitect-example","source_path":"./Example/MyNat.lean","lean4_code":"def add (a b : MyNat) : MyNat :=\n match b with\n | zero => a\n | succ b => succ (add a b)\n\n","line":14,"end_line":18,"proof_status":"formalized"} |
| {"id":"MyNat.zero_add","label":"MyNat.zero_add","background_color":"#1CAC78","border_color":"green","kind":"ellipse","dep_graph_url":"https://hanwenzhu.github.io/LeanArchitect-example/blueprint/dep_graph_document.html","dependencies":["def:nat-add"],"nlp_text":"For any natural number \\(a\\), \\(0 + a = a\\), where \\(+\\) is definition 2.","doc_url":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.zero_add","latex_link":"index.html#MyNat.zero_add","lean_link":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.zero_add","lean_decl_name":"MyNat.zero_add","kind_description":"theorems and lemmas","status_from_color":"formalized","lookup_in_mathlib4v4.22.0":false,"found_in_mathlib4v4.22.0":false,"source_repo":"LeanArchitect-example","source_path":"./Example/MyNat.lean","lean4_code":"theorem zero_add (a : MyNat) : add zero a = a := by\n /-- The proof follows by induction. -/\n induction a <;> simp [*, add]\n\n","line":21,"end_line":24,"proof_status":"formalized"} |
| {"id":"MyNat.mul","label":"MyNat.mul","background_color":"#A3D6FF","border_color":"blue","kind":"box","dep_graph_url":"https://hanwenzhu.github.io/LeanArchitect-example/blueprint/dep_graph_document.html","dependencies":["def:nat-add"],"nlp_text":"Natural number multiplication.","doc_url":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.mul","latex_link":"index.html#MyNat.mul","lean_link":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.mul","lean_decl_name":"MyNat.mul","kind_description":"definitions","status_from_color":"ready_to_formalize","lookup_in_mathlib4v4.22.0":false,"found_in_mathlib4v4.22.0":false,"source_repo":"LeanArchitect-example","source_path":"./Example/MyNat.lean","lean4_code":"def mul (a b : MyNat) : MyNat := sorry\n\n","line":49,"end_line":50,"proof_status":"statement_formalized"} |
| {"id":"MyNat.succ_add","label":"MyNat.succ_add","background_color":"#A3D6FF","border_color":"green","kind":"ellipse","dep_graph_url":"https://hanwenzhu.github.io/LeanArchitect-example/blueprint/dep_graph_document.html","dependencies":["def:nat-add"],"nlp_text":"For any natural numbers \\(a, b\\), \\((a + 1) + b = (a + b) + 1\\).","doc_url":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.succ_add","latex_link":"index.html#MyNat.succ_add","lean_link":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.succ_add","lean_decl_name":"MyNat.succ_add","kind_description":"theorems and lemmas","status_from_color":"ready_to_formalize","lookup_in_mathlib4v4.22.0":false,"found_in_mathlib4v4.22.0":false,"source_repo":"LeanArchitect-example","source_path":"./Example/MyNat.lean","lean4_code":"theorem succ_add (a b : MyNat) : add (succ a) b = succ (add a b) := by\n /-- Proof by induction on $b$. -/\n -- If the proof contains sorry, the `\\leanok` command will not be added\n sorry\n\n","line":27,"end_line":31,"proof_status":"statement_formalized"} |
| {"id":"MyNat.add_comm","label":"MyNat.add_comm","background_color":"#A3D6FF","border_color":"green","kind":"ellipse","dep_graph_url":"https://hanwenzhu.github.io/LeanArchitect-example/blueprint/dep_graph_document.html","dependencies":["MyNat.zero_add","MyNat.succ_add"],"nlp_text":"For any natural numbers \\(a, b\\), \\(a + b = b + a\\).","doc_url":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.add_comm","latex_link":"index.html#MyNat.add_comm","lean_link":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.add_comm","lean_decl_name":"MyNat.add_comm","kind_description":"theorems and lemmas","status_from_color":"ready_to_formalize","lookup_in_mathlib4v4.22.0":false,"found_in_mathlib4v4.22.0":false,"source_repo":"LeanArchitect-example","source_path":"./Example/MyNat.lean","lean4_code":"theorem add_comm (a b : MyNat) : add a b = add b a := by\n induction b with\n | zero =>\n have := trivial\n /-- The base case follows from \\cref{MyNat.zero_add}. -/\n simp [add]\n | succ b ih =>\n /-- The inductive case follows from \\cref{MyNat.succ_add}. -/\n sorry_using [succ_add] -- the `sorry_using` tactic declares that the proof uses succ_add\n\n/-! ## Multiplication -/\n\n","line":34,"end_line":45,"proof_status":"statement_formalized"} |
| {"id":"MyNat.mul_comm","label":"MyNat.mul_comm","background_color":"white","border_color":"green","kind":"ellipse","dep_graph_url":"https://hanwenzhu.github.io/LeanArchitect-example/blueprint/dep_graph_document.html","dependencies":["MyNat.mul"],"nlp_text":"For any natural numbers \\(a, b\\), \\(a * b = b * a\\).","doc_url":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.mul_comm","latex_link":"index.html#MyNat.mul_comm","lean_link":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.mul_comm","lean_decl_name":"MyNat.mul_comm","kind_description":"theorems and lemmas","status_from_color":"formalized","lookup_in_mathlib4v4.22.0":false,"found_in_mathlib4v4.22.0":false,"source_repo":"LeanArchitect-example","source_path":"./Example/MyNat.lean","lean4_code":"theorem mul_comm (a b : MyNat) : mul a b = mul b a := by sorry\n\n/-! ## Fermat's Last Theorem -/\n\n","line":53,"end_line":56,"proof_status":"formalized"} |
| {"id":"thm:flt","label":"flt","background_color":"white","border_color":"#FFAA33","kind":"ellipse","dep_graph_url":"https://hanwenzhu.github.io/LeanArchitect-example/blueprint/dep_graph_document.html","dependencies":["MyNat.mul_comm"],"nlp_text":"Fermat’s last theorem.","doc_url":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.flt","latex_link":"index.html#thm:flt","lean_link":"https://hanwenzhu.github.io/lean-architect-example/docs/find/#doc/MyNat.flt","lean_decl_name":"MyNat.flt","kind_description":"theorems and lemmas","status_from_color":"unknown","lookup_in_mathlib4v4.22.0":false,"found_in_mathlib4v4.22.0":false,"source_repo":"LeanArchitect-example","source_path":"./Example/MyNat.lean","lean4_code":"theorem flt : (sorry : Prop) := sorry\n\nend MyNat\n\n-- Finally, these are utility commands for debugging:\n\n","line":66,"end_line":71,"proof_status":"statement_formalized"} |
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