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@ -1,7 +1,7 @@
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import GameServer.Commands
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-- Wird im Level "Implication 11" ohne Beweis angenommen.
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LemmaDoc not_not as not_not in "Logic"
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LemmaDoc not_not as "not_not" in "Logic"
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"
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### Aussage
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@ -13,7 +13,7 @@ LemmaDoc not_not as not_not in "Logic"
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"
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-- Wird im Level "Implication 10" ohne Beweis angenommen.
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LemmaDoc not_or_of_imp as not_or_of_imp in "Logic"
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LemmaDoc not_or_of_imp as "not_or_of_imp" in "Logic"
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"
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### Aussage
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@ -26,7 +26,7 @@ LemmaDoc not_or_of_imp as not_or_of_imp in "Logic"
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"
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-- Wird im Level "Implication 12" bewiesen.
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LemmaDoc imp_iff_not_or as imp_iff_not_or in "Logic"
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LemmaDoc imp_iff_not_or as "imp_iff_not_or" in "Logic"
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"
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### Aussage
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@ -38,42 +38,42 @@ LemmaDoc imp_iff_not_or as imp_iff_not_or in "Logic"
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"
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LemmaDoc Nat.succ_pos as Nat.succ_pos in "Nat"
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LemmaDoc Nat.succ_pos as "Nat.succ_pos" in "Nat"
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"
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"
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LemmaDoc Nat.pos_iff_ne_zero as Nat.pos_iff_ne_zero in "Nat"
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LemmaDoc Nat.pos_iff_ne_zero as "Nat.pos_iff_ne_zero" in "Nat"
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"
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"
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LemmaDoc zero_add as zero_add in "Addition"
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LemmaDoc zero_add as "zero_add" in "Addition"
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"This lemma says `∀ a : ℕ, 0 + a = a`."
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LemmaDoc add_zero as add_zero in "Addition"
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LemmaDoc add_zero as "add_zero" in "Addition"
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"This lemma says `∀ a : ℕ, a + 0 = a`."
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LemmaDoc add_succ as add_succ in "Addition"
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LemmaDoc add_succ as "add_succ" in "Addition"
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"This lemma says `∀ a b : ℕ, a + succ b = succ (a + b)`."
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LemmaDoc not_forall as not_forall in "Logic"
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LemmaDoc not_forall as "not_forall" in "Logic"
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"`∀ (A : Prop), ¬(∀ x, A) ↔ ∃x, (¬A)`."
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LemmaDoc not_exists as not_exists in "Logic"
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LemmaDoc not_exists as "not_exists" in "Logic"
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"`∀ (A : Prop), ¬(∃ x, A) ↔ ∀x, (¬A)`."
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DefinitionDoc Even
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DefinitionDoc Even as "Even"
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"
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`even n` ist definiert als `∃ r, a = 2 * r`.
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Die Definition kann man mit `unfold even at *` einsetzen.
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"
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DefinitionDoc Odd
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DefinitionDoc Odd as "Odd"
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"
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`odd n` ist definiert als `∃ r, a = 2 * r + 1`.
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Die Definition kann man mit `unfold odd at *` einsetzen.
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"
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DefinitionDoc Injective
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DefinitionDoc Injective as "Injective"
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"
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`Injective f` ist definiert als
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@ -83,7 +83,7 @@ DefinitionDoc Injective
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definiert.
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"
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DefinitionDoc Surjective
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DefinitionDoc Surjective as "Surjective"
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"
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`Surjective f` ist definiert als
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@ -92,19 +92,19 @@ DefinitionDoc Surjective
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```
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"
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DefinitionDoc Bijective
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DefinitionDoc Bijective as "Bijective"
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"
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"
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DefinitionDoc LeftInverse
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DefinitionDoc LeftInverse as "LeftInverse"
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"
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"
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DefinitionDoc RightInverse
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DefinitionDoc RightInverse as "RightInverse"
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"
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"
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DefinitionDoc StrictMono
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DefinitionDoc StrictMono as "StrictMono"
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"
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`StrictMono f` ist definiert als
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@ -114,93 +114,93 @@ DefinitionDoc StrictMono
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"
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LemmaDoc even_iff_not_odd as even_iff_not_odd in "Nat"
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LemmaDoc even_iff_not_odd as "even_iff_not_odd" in "Nat"
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"`Even n ↔ ¬ (Odd n)`"
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LemmaDoc odd_iff_not_even as odd_iff_not_even in "Nat"
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LemmaDoc odd_iff_not_even as "odd_iff_not_even" in "Nat"
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"`Odd n ↔ ¬ (Even n)`"
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LemmaDoc even_square as even_square in "Nat"
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LemmaDoc even_square as "even_square" in "Nat"
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"`∀ (n : ℕ), Even n → Even (n ^ 2)`"
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LemmaDoc mem_univ as mem_univ in "Set"
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LemmaDoc mem_univ as "mem_univ" in "Set"
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"x ∈ @univ α"
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LemmaDoc not_mem_empty as not_mem_empty in "Set"
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LemmaDoc not_mem_empty as "not_mem_empty" in "Set"
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""
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LemmaDoc empty_subset as empty_subset in "Set"
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LemmaDoc empty_subset as "empty_subset" in "Set"
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""
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LemmaDoc Subset.antisymm_iff as Subset.antisymm_iff in "Set"
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LemmaDoc Subset.antisymm_iff as "Subset.antisymm_iff" in "Set"
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""
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LemmaDoc Nat.prime_def_lt'' as Nat.prime_def_lt'' in "Nat"
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LemmaDoc Nat.prime_def_lt'' as "Nat.prime_def_lt''" in "Nat"
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""
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LemmaDoc Finset.sum_add_distrib as Finset.sum_add_distrib in "Sum"
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LemmaDoc Finset.sum_add_distrib as "Finset.sum_add_distrib" in "Sum"
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""
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LemmaDoc Fin.sum_univ_castSucc as Fin.sum_univ_castSucc in "Sum"
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LemmaDoc Fin.sum_univ_castSucc as "Fin.sum_univ_castSucc" in "Sum"
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""
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LemmaDoc Nat.succ_eq_add_one as Nat.succ_eq_add_one in "Sum"
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LemmaDoc Nat.succ_eq_add_one as "Nat.succ_eq_add_one" in "Sum"
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""
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LemmaDoc add_comm as add_comm in "Nat"
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LemmaDoc add_comm as "add_comm" in "Nat"
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""
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LemmaDoc mul_add as mul_add in "Nat"
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LemmaDoc mul_add as "mul_add" in "Nat"
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""
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LemmaDoc add_mul as add_mul in "Nat"
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LemmaDoc add_mul as "add_mul" in "Nat"
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""
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LemmaDoc arithmetic_sum as arithmetic_sum in "Sum"
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LemmaDoc arithmetic_sum as "arithmetic_sum" in "Sum"
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""
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LemmaDoc add_pow_two as add_pow_two in "Nat"
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LemmaDoc add_pow_two as "add_pow_two" in "Nat"
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""
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LemmaDoc Finset.sum_comm as Finset.sum_comm in "Sum"
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LemmaDoc Finset.sum_comm as "Finset.sum_comm" in "Sum"
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""
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LemmaDoc Function.comp_apply as Function.comp_apply in "Function"
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LemmaDoc Function.comp_apply as "Function.comp_apply" in "Function"
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""
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LemmaDoc not_le as not_le in "Logic"
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LemmaDoc not_le as "not_le" in "Logic"
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""
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LemmaDoc if_pos as if_pos in "Logic"
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LemmaDoc if_pos as "if_pos" in "Logic"
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""
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LemmaDoc if_neg as if_neg in "Logic"
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LemmaDoc if_neg as "if_neg" in "Logic"
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""
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LemmaDoc StrictMono.injective as StrictMono.injective in "Function"
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LemmaDoc StrictMono.injective as "StrictMono.injective" in "Function"
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""
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LemmaDoc StrictMono.add as StrictMono.add in "Function"
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LemmaDoc StrictMono.add as "StrictMono.add" in "Function"
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""
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LemmaDoc Odd.strictMono_pow as Odd.strictMono_pow in "Function"
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LemmaDoc Odd.strictMono_pow as "Odd.strictMono_pow" in "Function"
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""
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LemmaDoc Exists.choose as Exists.choose in "Function"
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LemmaDoc Exists.choose as "Exists.choose" in "Function"
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""
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LemmaDoc Exists.choose_spec as Exists.choose_spec in "Function"
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LemmaDoc Exists.choose_spec as "Exists.choose_spec" in "Function"
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""
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LemmaDoc congrArg as congrArg in "Function"
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LemmaDoc congrArg as "congrArg" in "Function"
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""
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LemmaDoc congrFun as congrFun in "Function"
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LemmaDoc congrFun as "congrFun" in "Function"
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""
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LemmaDoc Iff.symm as Iff.symm in "Logic"
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LemmaDoc Iff.symm as "Iff.symm" in "Logic"
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""
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