fix missing lemma docs from statement names
This commit is contained in:
@@ -1,31 +1,31 @@
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import GameServer.Commands
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LemmaDoc MyNat.add_zero as "add_zero" in "Nat"
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""
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"(missing)"
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LemmaDoc MyNat.add_succ as "add_succ" in "Nat"
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""
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"(missing)"
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LemmaDoc MyNat.zero_add as "zero_add" in "Nat"
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""
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"(missing)"
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LemmaDoc MyNat.add_assoc as "add_assoc" in "Nat"
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""
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"(missing)"
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LemmaDoc MyNat.succ_add as "succ_add" in "Nat"
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""
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"(missing)"
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LemmaDoc MyNat.add_comm as "add_comm" in "Nat"
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""
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"(missing)"
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LemmaDoc MyNat.one_eq_succ_zero as "one_eq_succ_zero" in "Nat"
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""
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"(missing)"
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LemmaDoc not_iff_imp_false as "not_iff_imp_false" in "Prop"
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""
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"(missing)"
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LemmaDoc MyNat.succ_inj as "succ_inj" in "Nat"
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""
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"(missing)"
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LemmaDoc MyNat.zero_ne_succ as "zero_ne_succ" in "Nat"
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""
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"(missing)"
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@@ -36,7 +36,7 @@ note that `zero_add` is about zero add something, and `add_zero` is about someth
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The names of the proofs tell you what the theorems are. Anyway, let's prove `0 + n = n`.
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"
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Statement zero_add
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Statement MyNat.zero_add
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"For all natural numbers $n$, we have $0 + n = n$."
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(n : ℕ) : 0 + n = n := by
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Hint "You can start a proof by induction over `n` by typing:
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@@ -30,7 +30,7 @@ that addition, as defined the way we've defined it, is associative.
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See if you can prove associativity of addition.
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"
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Statement add_assoc
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Statement MyNat.add_assoc
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"On the set of natural numbers, addition is associative.
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In other words, for all natural numbers $a, b$ and $c$, we have
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$ (a + b) + c = a + (b + c). $"
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@@ -42,7 +42,7 @@ that `a + succ(b) = succ(a + b)`. The tactic `rw [add_succ]` just says to Lean \
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what the variables are\".
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"
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Statement succ_add
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Statement MyNat.succ_add
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"For all natural numbers $a, b$, we have
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$ \\operatorname{succ}(a) + b = \\operatorname{succ}(a + b)$."
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(a b : ℕ) : succ a + b = succ (a + b) := by
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@@ -29,7 +29,7 @@ Look in your inventory to see the proofs you have available.
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These should be enough.
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"
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Statement add_comm
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Statement MyNat.add_comm
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"On the set of natural numbers, addition is commutative.
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In other words, for all natural numbers $a$ and $b$, we have
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$a + b = b + a$."
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@@ -40,7 +40,7 @@ some theorems about $0$ (`zero_add`, `add_zero`), but, other than `1 = succ 0`,
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no theorems at all which mention $1$. Let's prove one now.
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"
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Statement succ_eq_add_one
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Statement --MyNat.succ_eq_add_one
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"For any natural number $n$, we have
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$ \\operatorname{succ}(n) = n+1$ ."
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(n : ℕ) : succ n = n + 1 := by
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@@ -35,7 +35,7 @@ additions of the form `a + ?`, and `rw add_comm a b,` will only
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swap additions of the form `a + b`.
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"
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Statement add_right_comm
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Statement --add_right_comm
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"For all natural numbers $a, b$ and $c$, we have
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$a + b + c = a + c + b$."
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(a b c : ℕ) : a + b + c = a + c + b := by
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@@ -17,7 +17,7 @@ theorem MyNat.succ_inj {a b : ℕ} : succ a = succ b → a = b := by simp only [
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theorem MyNat.zero_ne_succ (a : ℕ) : zero ≠ succ a := by simp only [ne_eq, not_false_iff]
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Statement succ_inj'
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Statement -- MyNat.succ_inj'
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""
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{a b : ℕ} (hs : succ a = succ b) : a = b := by
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exact succ_inj hs
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@@ -16,7 +16,7 @@ Introduction
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set_option tactic.hygienic false
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Statement and_symm
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Statement --and_symm
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""
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(P Q : Prop) : P ∧ Q → Q ∧ P := by
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intro h
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@@ -14,7 +14,7 @@ Introduction
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"
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Statement and_trans
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Statement --and_trans
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""
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(P Q R : Prop) : P ∧ Q → Q ∧ R → P ∧ R := by
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intro hpq
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@@ -14,7 +14,7 @@ Introduction
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"
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Statement iff_trans
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Statement --iff_trans
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""
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(P Q R : Prop) : (P ↔ Q) → (Q ↔ R) → (P ↔ R) := by
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intro hpq
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@@ -14,7 +14,7 @@ Introduction
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"
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Statement iff_trans
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Statement --iff_trans
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""
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(P Q R : Prop) : (P ↔ Q) → (Q ↔ R) → (P ↔ R) := by
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intro hpq hqr
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@@ -15,7 +15,7 @@ Introduction
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"
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Statement or_symm
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Statement --or_symm
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""
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(P Q : Prop) : P ∨ Q → Q ∨ P := by
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intro h
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@@ -15,7 +15,7 @@ Introduction
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"
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Statement and_or_distrib_left
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Statement --and_or_distrib_left
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""
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(P Q R : Prop) : P ∧ (Q ∨ R) ↔ (P ∧ Q) ∨ (P ∧ R) := by
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constructor
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@@ -17,7 +17,7 @@ Introduction
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"
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Statement contra
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Statement --contra
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""
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(P Q : Prop) : (P ∧ ¬ P) → Q := by
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intro h
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