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Mathlib.RingTheory.HahnSeries.Lex
{ "line": 418, "column": 47 }
{ "line": 418, "column": 58 }
[ { "pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : PartialOrder R\nΓ' : Type u_3\ninst✝¹ : LinearOrder Γ'\nf : Γ ↪o Γ'\ninst✝ : Zero R\na b : Lex R⟦Γ⟧\ni : Γ\nhj : ∀ j < i, (ofLex a).coeff j = (ofLex b).coeff j\nhi : (ofLex a).coeff i < (ofLex b).coeff i\n⊢ (embDomain f (ofLex a)).coeff (f i)...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.HahnSeries.Lex
{ "line": 421, "column": 10 }
{ "line": 421, "column": 21 }
[ { "pp": "case pos\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : PartialOrder R\nΓ' : Type u_3\ninst✝¹ : LinearOrder Γ'\nf : Γ ↪o Γ'\ninst✝ : Zero R\na b : Lex R⟦Γ⟧\ni : Γ\nhj : ∀ j < i, (ofLex a).coeff j = (ofLex b).coeff j\nhi : (ofLex a).coeff i < (ofLex b).coeff i\nj' : Γ\nhki : f j' < f i\n⊢...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Cone
{ "line": 69, "column": 39 }
{ "line": 69, "column": 50 }
[ { "pp": "T : Type u_1\ninst✝² : Ring T\ninst✝¹ : PartialOrder T\ninst✝ : IsOrderedRing T\na✝ a : T\n⊢ a ∈ (Subsemiring.nonneg T).carrier → -a ∈ (Subsemiring.nonneg T).carrier → a = 0", "usedConstants": [ "AddGroup.toSubtractionMonoid", "Eq.mpr", "NegZeroClass.toNeg", "NonAssocSemirin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Cone
{ "line": 91, "column": 49 }
{ "line": 91, "column": 60 }
[ { "pp": "S : Type u_1\nR : Type u_2\ninst✝² : Ring R\ninst✝¹ : SetLike S R\nC : S\ninst✝ : RingConeClass S R\nx✝ : PartialOrder R := PartialOrder.mkOfAddGroupCone C\nthis✝ : IsOrderedAddMonoid R\nthis : ZeroLEOneClass R\nx y : R\nxnn : 0 ≤ x\nynn : 0 ≤ y\n⊢ x * y - 0 ∈ C", "usedConstants": [ "Eq.mpr",...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 94, "column": 55 }
{ "line": 94, "column": 66 }
[ { "pp": "K : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimede...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 115, "column": 53 }
{ "line": 115, "column": 64 }
[ { "pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 116, "column": 53 }
{ "line": 116, "column": 64 }
[ { "pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 132, "column": 59 }
{ "line": 132, "column": 70 }
[ { "pp": "K : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimede...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 133, "column": 59 }
{ "line": 133, "column": 70 }
[ { "pp": "K : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimede...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 136, "column": 10 }
{ "line": 136, "column": 21 }
[ { "pp": "K : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimede...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 142, "column": 4 }
{ "line": 142, "column": 51 }
[ { "pp": "case pos\nK : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : Finit...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 145, "column": 4 }
{ "line": 145, "column": 15 }
[ { "pp": "case neg\nK : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : Finit...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 163, "column": 2 }
{ "line": 163, "column": 13 }
[ { "pp": "case h.e'_4.h\nK : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 168, "column": 61 }
{ "line": 168, "column": 72 }
[ { "pp": "K : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nthis : ⨆ i, u.baseD...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 171, "column": 2 }
{ "line": 171, "column": 13 }
[ { "pp": "case a.h\nK : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : Finit...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 208, "column": 4 }
{ "line": 208, "column": 15 }
[ { "pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 237, "column": 2 }
{ "line": 237, "column": 29 }
[ { "pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 244, "column": 2 }
{ "line": 244, "column": 13 }
[ { "pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 279, "column": 4 }
{ "line": 279, "column": 15 }
[ { "pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 285, "column": 4 }
{ "line": 285, "column": 15 }
[ { "pp": "case hyp\nK : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGro...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 299, "column": 4 }
{ "line": 299, "column": 15 }
[ { "pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Defs
{ "line": 159, "column": 13 }
{ "line": 159, "column": 49 }
[ { "pp": "R : Type u_1\ninst✝ : CommRing R\nP : RingPreordering R\nx✝ : P.HasIdealSupport\n⊢ ∀ (x a : R), a ∈ P → -a ∈ P → x * a ∈ P ∧ -(x * a) ∈ P", "usedConstants": [] } ]
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 302, "column": 4 }
{ "line": 302, "column": 15 }
[ { "pp": "case a\nK : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Defs
{ "line": 165, "column": 21 }
{ "line": 165, "column": 32 }
[ { "pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : HasMemOrNegMem P\nx a : R\nha : a ∈ P.supportAddSubgroup\nhx : x ∈ P\n⊢ x * a ∈ ↑P", "usedConstants": [ "Eq.mpr", "SetLike.mem_coe._simp_1", "HMul.hMul", "CommSemiring.toSemiring", "Membership.mem", ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Defs
{ "line": 165, "column": 53 }
{ "line": 165, "column": 64 }
[ { "pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : HasMemOrNegMem P\nx a : R\nha : a ∈ P.supportAddSubgroup\nhx : x ∈ P\n⊢ x * a ∈ -↑P", "usedConstants": [ "Eq.mpr", "SetLike.mem_coe._simp_1", "NonUnitalCommRing.toNonUnitalNonAssocCommRing", "HMul.hMul", ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Defs
{ "line": 166, "column": 21 }
{ "line": 166, "column": 32 }
[ { "pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : HasMemOrNegMem P\nx a : R\nha : a ∈ P.supportAddSubgroup\nhx : -x ∈ P\n⊢ x * a ∈ ↑P", "usedConstants": [ "Eq.mpr", "SetLike.mem_coe._simp_1", "HMul.hMul", "CommSemiring.toSemiring", "Membership.mem", ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Defs
{ "line": 166, "column": 53 }
{ "line": 166, "column": 64 }
[ { "pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : HasMemOrNegMem P\nx a : R\nha : a ∈ P.supportAddSubgroup\nhx : -x ∈ P\n⊢ x * a ∈ -↑P", "usedConstants": [ "Eq.mpr", "SetLike.mem_coe._simp_1", "NonUnitalCommRing.toNonUnitalNonAssocCommRing", "HMul.hMul", ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Defs
{ "line": 179, "column": 18 }
{ "line": 179, "column": 29 }
[ { "pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : P.HasIdealSupport\n⊢ ∀ (c : R) {x : R}, x ∈ P.supportAddSubgroup.carrier → c • x ∈ P.supportAddSubgroup.carrier", "usedConstants": [ "Eq.mpr", "instHSMul", "Semiring.toModule", "HMul.hMul", "AddSubsemigr...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 316, "column": 62 }
{ "line": 316, "column": 73 }
[ { "pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 317, "column": 62 }
{ "line": 317, "column": 73 }
[ { "pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 321, "column": 8 }
{ "line": 321, "column": 19 }
[ { "pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Archimedean
{ "line": 121, "column": 2 }
{ "line": 121, "column": 71 }
[ { "pp": "case mk.mk\nR : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : CommRing R\ninst✝ : IsStrictOrderedRing R\nx : R\nhx : x ≠ 0\ny z : R\nhyz : (fun x_1 ↦ mk x + x_1) (mk y) = (fun x_1 ↦ mk x + x_1) (mk z)\n⊢ mk y = mk z", "usedConstants": [ "Eq.mpr", "NonAssocSemiring.toAddCommMonoidWithOne", ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 325, "column": 6 }
{ "line": 325, "column": 17 }
[ { "pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Archimedean
{ "line": 156, "column": 2 }
{ "line": 156, "column": 13 }
[ { "pp": "R : Type u_1\ninst✝⁶ : LinearOrder R\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\nf : S →+*o R\nx : S\nh : x ≠ 0\n⊢ mk (f x) = 0", "usedConstants": [] } ]
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Archimedean
{ "line": 170, "column": 2 }
{ "line": 170, "column": 13 }
[ { "pp": "R : Type u_1\ninst✝⁶ : LinearOrder R\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\nf : S →+*o R\ny : S\n⊢ 0 ≤ mk (f y)", "usedConstants": [] } ]
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Archimedean
{ "line": 176, "column": 4 }
{ "line": 176, "column": 15 }
[ { "pp": "case hpos\nR : Type u_1\ninst✝⁶ : LinearOrder R\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\nf : S →+*o R\nx : R\nhx : 0 < mk x\ny : S\nhy : 0 < y\n⊢ 0 ≤ f y", "usedConstants":...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Archimedean
{ "line": 182, "column": 4 }
{ "line": 182, "column": 15 }
[ { "pp": "case hneg\nR : Type u_1\ninst✝⁶ : LinearOrder R\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\nf : S →+*o R\nx : R\nhx : 0 < mk x\ny : S\nhy : y < 0\n⊢ f y ≤ 0", "usedConstants":...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Archimedean
{ "line": 209, "column": 2 }
{ "line": 209, "column": 13 }
[ { "pp": "R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : CommRing R\ninst✝ : IsStrictOrderedRing R\nx : R\nn : ℕ\nhn : |ArchimedeanOrder.val (ArchimedeanOrder.of x)| ≤ n • |ArchimedeanOrder.val (ArchimedeanOrder.of 1)|\n⊢ |x| ≤ ↑n", "usedConstants": [] } ]
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 329, "column": 4 }
{ "line": 329, "column": 27 }
[ { "pp": "case neg\nK : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGro...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Archimedean
{ "line": 256, "column": 37 }
{ "line": 256, "column": 48 }
[ { "pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : LinearOrder R\ninst✝⁶ : LinearOrder S\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\ninst✝³ : Ring S\ninst✝² : IsStrictOrderedRing S\ninst✝¹ : DenselyOrdered R\ninst✝ : Archimedean R\nx y : S\nf : R →+* S\nhf : StrictMono ⇑f\nq : R\n⊢ 0 < f q ↔ 0 < q", "u...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.HahnSeries.Multiplication
{ "line": 437, "column": 4 }
{ "line": 437, "column": 33 }
[ { "pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nS : Type u_4\nV : Type u_5\ninst✝³ : AddCommMonoid Γ\ninst✝² : PartialOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : NonUnitalNonAssocSemiring R\nx y z : R⟦Γ⟧\n⊢ (HahnModule.of R).symm ((x + y) • (HahnModule.of R) z) =\n (HahnModule.of R).symm (x • (...
refine HahnModule.add_smul ?_
Lean.Elab.Tactic.evalRefine
Lean.Parser.Tactic.refine
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 272, "column": 32 }
{ "line": 329, "column": 62 }
[ { "pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst...
by -- decompose `x` to sum of `stratum` have hmem : x.val ∈ seed.baseEmbedding.domain := x.prop simp_rw [seed.domain_baseEmbedding] at hmem obtain ⟨f, hf⟩ := (Submodule.mem_iSup_iff_exists_dfinsupp' _ _).mp hmem have hfpos : 0 < (f.sum fun _ x ↦ x.val) := by rw [hf] simpa using hx have hsupport : f....
[anonymous]
Lean.Parser.Term.byTactic
Mathlib.Algebra.Order.Ring.Archimedean
{ "line": 262, "column": 6 }
{ "line": 262, "column": 31 }
[ { "pp": "case mp.succ\nR : Type u_1\nS : Type u_2\ninst✝⁷ : LinearOrder R\ninst✝⁶ : LinearOrder S\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\ninst✝³ : Ring S\ninst✝² : IsStrictOrderedRing S\ninst✝¹ : DenselyOrdered R\ninst✝ : Archimedean R\nx y : S\nf : R →+* S\nhf : StrictMono ⇑f\nH : ∀ {q : R}, 0 < ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 336, "column": 34 }
{ "line": 336, "column": 45 }
[ { "pp": "K : Type u_1\ninst✝¹² : DivisionRing K\ninst✝¹¹ : LinearOrder K\ninst✝¹⁰ : IsOrderedRing K\ninst✝⁹ : Archimedean K\nM : Type u_2\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : LinearOrder M\ninst✝⁶ : IsOrderedAddMonoid M\ninst✝⁵ : Module K M\ninst✝⁴ : IsOrderedModule K M\nR : Type u_3\ninst✝³ : AddCommGroup R\nins...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.HahnSeries.Multiplication
{ "line": 474, "column": 2 }
{ "line": 474, "column": 13 }
[ { "pp": "Γ' : Type u_2\nR : Type u_3\ninst✝³ : NonUnitalNonAssocSemiring R\ninst✝² : PartialOrder Γ'\ninst✝¹ : AddCommGroup Γ'\ninst✝ : IsOrderedAddMonoid Γ'\nr : R\nx : R⟦Γ'⟧\na b : Γ'\n⊢ ((single b) r * x).coeff a = r * x.coeff (a - b)", "usedConstants": [] } ]
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.HahnSeries.Multiplication
{ "line": 479, "column": 2 }
{ "line": 479, "column": 13 }
[ { "pp": "Γ' : Type u_2\nR : Type u_3\ninst✝³ : NonUnitalNonAssocSemiring R\ninst✝² : PartialOrder Γ'\ninst✝¹ : AddCommGroup Γ'\ninst✝ : IsOrderedAddMonoid Γ'\nr : R\nx : R⟦Γ'⟧\na b : Γ'\n⊢ (x * (single b) r).coeff a = x.coeff (a - b) * r", "usedConstants": [] } ]
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Archimedean
{ "line": 270, "column": 4 }
{ "line": 270, "column": 37 }
[ { "pp": "case mpr\nR : Type u_1\nS : Type u_2\ninst✝⁷ : LinearOrder R\ninst✝⁶ : LinearOrder S\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\ninst✝³ : Ring S\ninst✝² : IsStrictOrderedRing S\ninst✝¹ : DenselyOrdered R\ninst✝ : Archimedean R\nx y : S\nf : R →+* S\nhf : StrictMono ⇑f\nH : ∀ {q : R}, 0 < f q ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Archimedean
{ "line": 284, "column": 30 }
{ "line": 284, "column": 41 }
[ { "pp": "R : Type u_1\nS : Type u_2\ninst✝³ : LinearOrder R\ninst✝² : LinearOrder S\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nx y : R\nh : mk x = mk y\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ mk x ≠ ⊤", "usedConstants": [ "Eq.mpr", "congrArg", "ArchimedeanClass.instLinearOrder", "PartialOrder.to...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Archimedean
{ "line": 324, "column": 2 }
{ "line": 324, "column": 13 }
[ { "pp": "R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nq : ℚ\nh : q ≠ 0\n⊢ mk ↑q = 0", "usedConstants": [] } ]
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Archimedean
{ "line": 323, "column": 59 }
{ "line": 324, "column": 87 }
[ { "pp": "R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nq : ℚ\nh : q ≠ 0\n⊢ mk ↑q = 0", "usedConstants": [ "RingHom.instRingHomClass", "IsDomain.to_noZeroDivisors", "OrderAddMonoidHom.mk", "DivisionRing.toRatCast", "ZeroHom.toFun", "congr...
by simpa using mk_map_of_archimedean ⟨(Rat.castHom R).toAddMonoidHom, fun _ ↦ by simp⟩ h
[anonymous]
Lean.Parser.Term.byTactic
Mathlib.Algebra.Order.Ring.Archimedean
{ "line": 332, "column": 2 }
{ "line": 332, "column": 13 }
[ { "pp": "R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nx y : R\n⊢ mk x ≤ mk y ↔ ∃ q, 0 < q ∧ ↑q * |y| ≤ |x|", "usedConstants": [] } ]
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.HahnSeries.Multiplication
{ "line": 700, "column": 8 }
{ "line": 700, "column": 39 }
[ { "pp": "case inr.refine_1\nΓ✝ : Type u_1\nΓ' : Type u_2\nR✝ : Type u_3\nS : Type u_4\nV : Type u_5\nΓ : Type ?u.175106\nR : Type ?u.175372\ninst✝³ : LinearOrder Γ\ninst✝² : AddCommMonoid Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\ny : R⟦Γ⟧ˣ\nh : y ∈ {x | 0 < (↑x - 1).orderTop}\nh✝ : Nontrivial ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.HahnSeries.Multiplication
{ "line": 701, "column": 8 }
{ "line": 701, "column": 39 }
[ { "pp": "case inr.refine_2\nΓ✝ : Type u_1\nΓ' : Type u_2\nR✝ : Type u_3\nS : Type u_4\nV : Type u_5\nΓ : Type ?u.175106\nR : Type ?u.175372\ninst✝³ : LinearOrder Γ\ninst✝² : AddCommMonoid Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\ny : R⟦Γ⟧ˣ\nh : y ∈ {x | 0 < (↑x - 1).orderTop}\nh✝ : Nontrivial ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Basic
{ "line": 81, "column": 23 }
{ "line": 81, "column": 34 }
[ { "pp": "R✝¹ : Type u_1\ninst✝² : CommRing R✝¹\nP✝¹ : RingPreordering R✝¹\nR✝ : Type u_2\ninst✝¹ : CommRing R✝\nP✝ : Set R✝\nadd✝ : ?m.2\nmul✝ : ?m.3\nsq✝ : ?m.4\nneg_one✝ : ?m.5\nR : Type u_3\ninst✝ : CommRing R\nP : Set R\nadd : ∀ {x y : R}, x ∈ P → y ∈ P → x + y ∈ P\nmul : ∀ {x y : R}, x ∈ P → y ∈ P → x * y ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Basic
{ "line": 83, "column": 17 }
{ "line": 83, "column": 28 }
[ { "pp": "R✝¹ : Type u_1\ninst✝² : CommRing R✝¹\nP✝¹ : RingPreordering R✝¹\nR✝ : Type u_2\ninst✝¹ : CommRing R✝\nP✝ : Set R✝\nadd✝ : ?m.2\nmul✝ : ?m.3\nsq✝ : ?m.4\nneg_one✝ : ?m.5\nR : Type u_3\ninst✝ : CommRing R\nP : Set R\nadd : ∀ {x y : R}, x ∈ P → y ∈ P → x + y ∈ P\nmul : ∀ {x y : R}, x ∈ P → y ∈ P → x * y ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Basic
{ "line": 80, "column": 23 }
{ "line": 80, "column": 34 }
[ { "pp": "R✝¹ : Type u_1\ninst✝² : CommRing R✝¹\nP✝¹ : RingPreordering R✝¹\nR✝ : Type u_2\ninst✝¹ : CommRing R✝\nP✝ : Set R✝\nadd✝ : ?m.2\nmul✝ : ?m.3\nsq✝ : ?m.4\nneg_one✝ : ?m.5\nR : Type u_3\ninst✝ : CommRing R\nP : Set R\nadd : ∀ {x y : R}, x ∈ P → y ∈ P → x + y ∈ P\nmul : ∀ {x y : R}, x ∈ P → y ∈ P → x * y ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Basic
{ "line": 82, "column": 18 }
{ "line": 82, "column": 29 }
[ { "pp": "R✝¹ : Type u_1\ninst✝² : CommRing R✝¹\nP✝¹ : RingPreordering R✝¹\nR✝ : Type u_2\ninst✝¹ : CommRing R✝\nP✝ : Set R✝\nadd✝ : ?m.2\nmul✝ : ?m.3\nsq✝ : ?m.4\nneg_one✝ : ?m.5\nR : Type u_3\ninst✝ : CommRing R\nP : Set R\nadd : ∀ {x y : R}, x ∈ P → y ∈ P → x + y ∈ P\nmul : ∀ {x y : R}, x ∈ P → y ∈ P → x * y ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Basic
{ "line": 102, "column": 2 }
{ "line": 102, "column": 13 }
[ { "pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : P.HasIdealSupport\n⊢ 1 ∉ P.support", "usedConstants": [] } ]
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Basic
{ "line": 109, "column": 2 }
{ "line": 109, "column": 13 }
[ { "pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : P.HasIdealSupport\n⊢ Submodule.toAddSubgroup P.support ≠ Submodule.toAddSubgroup ⊤", "usedConstants": [ "Eq.mpr", "Submodule", "Semiring.toModule", "congrArg", "CommSemiring.toSemiring", "AddCommGr...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Basic
{ "line": 165, "column": 2 }
{ "line": 165, "column": 45 }
[ { "pp": "F : Type u_2\ninst✝ : Field F\nP : RingPreordering F\n⊢ P.support = ⊥", "usedConstants": [ "Eq.mpr", "AddSubgroup.instBot", "Semiring.toModule", "CommSemiring.toSemiring", "_private.Mathlib.Algebra.Order.Ring.Ordering.Basic.0.RingPreordering.support_eq_bot._simp_1_1", ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Basic
{ "line": 167, "column": 35 }
{ "line": 167, "column": 46 }
[ { "pp": "R : Type u_1\ninst✝¹ : CommRing R\nP✝ : RingPreordering R\nF : Type u_2\ninst✝ : Field F\nP : RingPreordering F\n⊢ P.support.IsPrime", "usedConstants": [ "Eq.mpr", "Semiring.toModule", "congrArg", "CommSemiring.toSemiring", "id", "Bot.bot", "Ideal", "...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Ring.Ordering.Basic
{ "line": 175, "column": 27 }
{ "line": 175, "column": 38 }
[ { "pp": "R : Type u_1\ninst✝ : CommRing R\nP : RingPreordering R\nx✝¹ : P.IsOrdering\na b : R\nx✝ : -(a * b) ∈ P\nthis : ¬(a ∈ P ∨ b ∈ P)\n⊢ a * b ∈ P", "usedConstants": [] } ]
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 461, "column": 30 }
{ "line": 461, "column": 41 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 467, "column": 4 }
{ "line": 467, "column": 15 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 473, "column": 4 }
{ "line": 473, "column": 15 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 498, "column": 2 }
{ "line": 498, "column": 13 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 498, "column": 21 }
{ "line": 498, "column": 32 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 551, "column": 2 }
{ "line": 551, "column": 44 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 574, "column": 4 }
{ "line": 574, "column": 15 }
[ { "pp": "case h.e'_2\nK : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCo...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 578, "column": 2 }
{ "line": 578, "column": 13 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 603, "column": 58 }
{ "line": 603, "column": 69 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 636, "column": 4 }
{ "line": 636, "column": 24 }
[ { "pp": "case hy\nK : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGr...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Star.Conjneg
{ "line": 62, "column": 38 }
{ "line": 62, "column": 49 }
[ { "pp": "G : Type u_2\nR : Type u_3\ninst✝² : AddGroup G\ninst✝¹ : CommSemiring R\ninst✝ : StarRing R\nf : G → R\n⊢ f = conjneg 1 ↔ f = 1", "usedConstants": [ "Eq.mpr", "NonAssocSemiring.toAddCommMonoidWithOne", "conjneg_one", "congrArg", "CommSemiring.toSemiring", "conjn...
conjneg_one
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 695, "column": 41 }
{ "line": 695, "column": 74 }
[ { "pp": "case coeff.h.inr\nK : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : ...
HahnSeries.coeff_truncLT_of_le hd
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 699, "column": 47 }
{ "line": 699, "column": 58 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 728, "column": 4 }
{ "line": 728, "column": 24 }
[ { "pp": "case refine_1.hy\nK : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : ...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 731, "column": 4 }
{ "line": 731, "column": 22 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 743, "column": 4 }
{ "line": 743, "column": 15 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 746, "column": 4 }
{ "line": 746, "column": 15 }
[ { "pp": "case a\nK : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGro...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 749, "column": 6 }
{ "line": 749, "column": 35 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 754, "column": 4 }
{ "line": 754, "column": 15 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Sub.Unbundled.Hom
{ "line": 36, "column": 2 }
{ "line": 36, "column": 33 }
[ { "pp": "R : Type u_3\ninst✝⁴ : NonUnitalCommSemiring R\ninst✝³ : Preorder R\ninst✝² : Sub R\ninst✝¹ : OrderedSub R\ninst✝ : MulLeftMono R\na b c : R\n⊢ a * c - b * c ≤ (a - b) * c", "usedConstants": [ "Eq.mpr", "HMul.hMul", "congrArg", "HSub.hSub", "Preorder.toLE", "id",...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 810, "column": 40 }
{ "line": 810, "column": 51 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 811, "column": 32 }
{ "line": 811, "column": 43 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 831, "column": 23 }
{ "line": 831, "column": 34 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 839, "column": 6 }
{ "line": 839, "column": 17 }
[ { "pp": "case pos.coeff.h.inl\nK : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 843, "column": 19 }
{ "line": 843, "column": 30 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 853, "column": 46 }
{ "line": 853, "column": 57 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.Valuation.ValuationSubring
{ "line": 53, "column": 4 }
{ "line": 53, "column": 16 }
[ { "pp": "K : Type u\ninst✝ : Field K\nA : ValuationSubring K\n⊢ Function.Injective fun A ↦ ↑A.toSubring", "usedConstants": [ "ValuationSubring" ] } ]
intro ⟨_, _⟩
Lean.Elab.Tactic.evalIntro
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 869, "column": 44 }
{ "line": 869, "column": 55 }
[ { "pp": "K : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGroup R\nin...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.Valuation.ValuationSubring
{ "line": 163, "column": 38 }
{ "line": 163, "column": 49 }
[ { "pp": "case a\nK : Type u\ninst✝ : Field K\nA : ValuationSubring K\na b : ↥A\nh : (algebraMap (↥A) K) a = (algebraMap (↥A) K) b\n⊢ ↑(↑1 * a) = ↑(↑1 * b)", "usedConstants": [ "Eq.mpr", "HMul.hMul", "Monoid.toMulOneClass", "congrArg", "CommSemiring.toSemiring", "Membershi...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.Valuation.ValuationSubring
{ "line": 163, "column": 30 }
{ "line": 163, "column": 51 }
[ { "pp": "K : Type u\ninst✝ : Field K\nA : ValuationSubring K\na b : ↥A\nh : (algebraMap (↥A) K) a = (algebraMap (↥A) K) b\n⊢ ↑1 * a = ↑1 * b", "usedConstants": [ "Eq.mpr", "HMul.hMul", "Algebra.algebraMap", "Monoid.toMulOneClass", "congrArg", "CommSemiring.toSemiring", ...
by ext; simpa using h
[anonymous]
Lean.Parser.Term.byTactic
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 892, "column": 4 }
{ "line": 892, "column": 35 }
[ { "pp": "case a\nK : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGro...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 897, "column": 2 }
{ "line": 897, "column": 13 }
[ { "pp": "case a\nK : Type u_1\ninst✝¹³ : DivisionRing K\ninst✝¹² : LinearOrder K\ninst✝¹¹ : IsOrderedRing K\ninst✝¹⁰ : Archimedean K\nM : Type u_2\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : LinearOrder M\ninst✝⁷ : IsOrderedAddMonoid M\ninst✝⁶ : Module K M\ninst✝⁵ : IsOrderedModule K M\nR : Type u_3\ninst✝⁴ : AddCommGro...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.Valuation.ValuationSubring
{ "line": 341, "column": 8 }
{ "line": 341, "column": 39 }
[ { "pp": "case h.mp.a.ha\nK : Type u\ninst✝ : Field K\nR S : ValuationSubring K\nh : R ≤ S\na r : ↥R\nhr : r ∈ (R.idealOfLE S h).primeCompl\n⊢ 0 < S.valuation ((algebraMap (↥R) K) r)", "usedConstants": [ "Eq.mpr", "GroupWithZero.toMonoidWithZero", "LinearOrderedCommGroupWithZero.toLinearOrd...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.Valuation.ValuationSubring
{ "line": 452, "column": 38 }
{ "line": 452, "column": 49 }
[ { "pp": "case mp.h\nK : Type u\ninst✝² : Field K\nΓ₁ : Type u_2\nΓ₂ : Type u_3\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₁\ninst✝ : LinearOrderedCommGroupWithZero Γ₂\nv₁ : Valuation K Γ₁\nv₂ : Valuation K Γ₂\nx : K\nh : v₁ x ≤ v₁ 1 ↔ v₂ x ≤ v₂ 1\n⊢ x ∈ v₁.valuationSubring ↔ x ∈ v₂.valuationSubring", "usedCo...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.Valuation.ValuationSubring
{ "line": 456, "column": 4 }
{ "line": 456, "column": 15 }
[ { "pp": "case mpr.h\nK : Type u\ninst✝² : Field K\nΓ₁ : Type u_2\nΓ₂ : Type u_3\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₁\ninst✝ : LinearOrderedCommGroupWithZero Γ₂\nv₁ : Valuation K Γ₁\nv₂ : Valuation K Γ₂\nh : v₁.valuationSubring = v₂.valuationSubring\nx : K\nthis : x ∈ v₁.valuationSubring ↔ x ∈ v₂.valuatio...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.Algebra.Order.Module.HahnEmbedding
{ "line": 965, "column": 2 }
{ "line": 965, "column": 29 }
[ { "pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.Valuation.ValuationSubring
{ "line": 525, "column": 6 }
{ "line": 525, "column": 17 }
[ { "pp": "case neg.inl\nK : Type u\ninst✝ : Field K\nA B : ValuationSubring K\nh : A.unitGroup ≤ B.unitGroup\nx : K\nh_1 : ¬x = 0\nh_2 : ¬1 + x = 0\nhx : A.valuation x < 1\nthis : Units.mk0 (1 + x) h_2 ∈ B.unitGroup\n⊢ x ∈ B", "usedConstants": [] } ]
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null
Mathlib.RingTheory.Valuation.ValuationSubring
{ "line": 532, "column": 4 }
{ "line": 532, "column": 15 }
[ { "pp": "case mpr\nK : Type u\ninst✝ : Field K\nA B : ValuationSubring K\nh : A ≤ B\nx : Kˣ\nhx : (A.mapOfLE B h) (A.valuation ↑x) = (A.mapOfLE B h) 1\n⊢ x ∈ B.unitGroup", "usedConstants": [ "Units.val", "Eq.mpr", "LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero", "V...
simpa using
Lean.Elab.Tactic.Simpa.evalSimpa
null