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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Invertible.sym.json

@@ -0,0 +1 @@
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{R : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Invertible.3958582437._hygCtx._hyg.3 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Order.Invertible.3958582437._hygCtx._hyg.6 : LinearOrder.{u_1} R] [inst._@.Mathlib.Algebra.Order.Invertible.3958582437._hygCtx._hyg.9 : IsStrictOrderedRing.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.3958582437._hygCtx._hyg.3 (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.3958582437._hygCtx._hyg.6))))] {a : R} [inst._@.Mathlib.Algebra.Order.Invertible.3958582437._hygCtx._hyg.13 : Invertible.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.3958582437._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R 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inst._@.Mathlib.Algebra.Order.Invertible.3958582437._hygCtx._hyg.13) (OfNat.ofNat.{u_1} R 0 (Zero.toOfNat0.{u_1} R (MulZeroClass.toZero.{u_1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.3958582437._hygCtx._hyg.3))))))) (LT.lt.{u_1} R (Preorder.toLT.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.3958582437._hygCtx._hyg.6)))))) a (OfNat.ofNat.{u_1} R 0 (Zero.toOfNat0.{u_1} R (MulZeroClass.toZero.{u_1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.3958582437._hygCtx._hyg.3)))))))","typeFull":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  (⅟a < 0) = (a < 0)","typeReadable":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  (⅟a < 0) = (a < 0)","typeReferences":[["PartialOrder","toPreorder"],["IsStrictOrderedRing"],["Lattice","toSemilatticeInf"],["Invertible","invOf"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Preorder","toLT"],["LinearOrder"],["OfNat","ofNat"],["LT","lt"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Semiring","toNonAssocSemiring"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["AddMonoidWithOne","toOne"],["Zero","toOfNat0"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Invertible"],["Semiring"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["Invertible","invOf"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Preorder","toLT"],["OfNat","ofNat"],["LT","lt"],["instDistribLatticeOfLinearOrder"],["invOf_lt_zero"],["DistribLattice","toLattice"],["Semiring","toNonAssocSemiring"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["AddMonoidWithOne","toOne"],["Zero","toOfNat0"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocSemiring","toAddCommMonoidWithOne"],["propext"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["invOf_le_one","_simp_1"],"typeFallback":"forall {R : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.6 : LinearOrder.{u_1} R] [inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.9 : IsStrictOrderedRing.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3 (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.6))))] {a : R} [inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.13 : Invertible.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3)))) a], (LE.le.{u_1} R (Preorder.toLE.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.6)))))) (OfNat.ofNat.{u_1} R 1 (One.toOfNat1.{u_1} R (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3)))))) a) -> (Eq.{1} Prop (LE.le.{u_1} R (Preorder.toLE.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.6)))))) (Invertible.invOf.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3)))) a inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.13) (OfNat.ofNat.{u_1} R 1 (One.toOfNat1.{u_1} R (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3))))))) True)","typeFull":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  1 ≤ a → (⅟a ≤ 1) = True","typeReadable":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  1 ≤ a → (⅟a ≤ 1) = True","typeReferences":[["PartialOrder","toPreorder"],["IsStrictOrderedRing"],["Lattice","toSemilatticeInf"],["True"],["Invertible","invOf"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearOrder"],["OfNat","ofNat"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["LE","le"],["AddMonoidWithOne","toOne"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["Preorder","toLE"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Invertible"],["Semiring"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["invOf_le_one"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["Invertible","invOf"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["eq_true"],["OfNat","ofNat"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["AddMonoidWithOne","toOne"],["LE","le"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Preorder","toLE"],["NonAssocSemiring","toAddCommMonoidWithOne"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["invOf_pos","_simp_1"],"typeFallback":"forall {R : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.3 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.6 : LinearOrder.{u_1} R] [inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.9 : IsStrictOrderedRing.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.3 (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.6))))] {a : R} [inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.13 : Invertible.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.3)))) a], Eq.{1} Prop (LT.lt.{u_1} R (Preorder.toLT.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.6)))))) (OfNat.ofNat.{u_1} R 0 (Zero.toOfNat0.{u_1} R (MulZeroClass.toZero.{u_1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.3)))))) (Invertible.invOf.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.3)))) a inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.13)) (LT.lt.{u_1} R (Preorder.toLT.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.6)))))) (OfNat.ofNat.{u_1} R 0 (Zero.toOfNat0.{u_1} R (MulZeroClass.toZero.{u_1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.3)))))) a)","typeFull":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  (0 < ⅟a) = (0 < a)","typeReadable":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  (0 < ⅟a) = (0 < a)","typeReferences":[["PartialOrder","toPreorder"],["IsStrictOrderedRing"],["Lattice","toSemilatticeInf"],["Invertible","invOf"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Preorder","toLT"],["LinearOrder"],["OfNat","ofNat"],["LT","lt"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Semiring","toNonAssocSemiring"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["AddMonoidWithOne","toOne"],["Zero","toOfNat0"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Invertible"],["Semiring"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["NonUnitalNonAssocSemiring","toDistrib"],["Invertible","invOf"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Preorder","toLT"],["OfNat","ofNat"],["LT","lt"],["invOf_pos"],["instDistribLatticeOfLinearOrder"],["Semiring","toNonAssocSemiring"],["DistribLattice","toLattice"],["MulZeroClass","toZero"],["AddMonoidWithOne","toOne"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["Zero","toOfNat0"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocSemiring","toAddCommMonoidWithOne"],["propext"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["invOf_le_one"],"typeFallback":"forall {R : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.6 : LinearOrder.{u_1} R] [inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.9 : IsStrictOrderedRing.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3 (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.6))))] {a : R} [inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.13 : Invertible.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3)))) a], (LE.le.{u_1} R (Preorder.toLE.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.6)))))) (OfNat.ofNat.{u_1} R 1 (One.toOfNat1.{u_1} R (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3)))))) a) -> (LE.le.{u_1} R (Preorder.toLE.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.6)))))) (Invertible.invOf.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3)))) a inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.13) (OfNat.ofNat.{u_1} R 1 (One.toOfNat1.{u_1} R (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.2199240063._hygCtx._hyg.3)))))))","typeFull":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  1 ≤ a → ⅟a ≤ 1","typeReadable":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  1 ≤ a → ⅟a ≤ 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(NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.100075680._hygCtx._hyg.3)))) a inst._@.Mathlib.Algebra.Order.Invertible.100075680._hygCtx._hyg.13) (OfNat.ofNat.{u_1} R 1 (One.toOfNat1.{u_1} R (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.100075680._hygCtx._hyg.3)))))))","typeFull":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  1 < a → ⅟a < 1","typeReadable":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  1 < a → ⅟a < 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{R : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.3 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.6 : LinearOrder.{u_1} R] [inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.9 : IsStrictOrderedRing.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.3 (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.6))))] {a : R} [inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.13 : Invertible.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.3)))) a], Iff (LT.lt.{u_1} R (Preorder.toLT.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.6)))))) (OfNat.ofNat.{u_1} R 0 (Zero.toOfNat0.{u_1} R (MulZeroClass.toZero.{u_1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.1324732627._hygCtx._hyg.3)))))) (Invertible.invOf.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R 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: Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  0 < ⅟a ↔ 0 < a","typeReadable":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  0 < ⅟a ↔ 0 < 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(NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.100075680._hygCtx._hyg.3)))) a], (LT.lt.{u_1} R (Preorder.toLT.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.100075680._hygCtx._hyg.6)))))) (OfNat.ofNat.{u_1} R 1 (One.toOfNat1.{u_1} R (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.100075680._hygCtx._hyg.3)))))) a) -> (Eq.{1} Prop (LT.lt.{u_1} R (Preorder.toLT.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R 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[IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  1 < a → (⅟a < 1) = True","typeReadable":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  1 < a → (⅟a < 1) = 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LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  (⅟a ≤ 0) = (a ≤ 0)","typeReadable":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  (⅟a ≤ 0) = (a ≤ 0)","typeReferences":[["PartialOrder","toPreorder"],["IsStrictOrderedRing"],["Lattice","toSemilatticeInf"],["Invertible","invOf"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearOrder"],["OfNat","ofNat"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Semiring","toNonAssocSemiring"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["LE","le"],["AddMonoidWithOne","toOne"],["Zero","toOfNat0"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Preorder","toLE"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Invertible"],["Semiring"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["Invertible","invOf"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["OfNat","ofNat"],["instDistribLatticeOfLinearOrder"],["invOf_nonpos"],["DistribLattice","toLattice"],["Semiring","toNonAssocSemiring"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["AddMonoidWithOne","toOne"],["LE","le"],["Zero","toOfNat0"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Preorder","toLE"],["NonAssocSemiring","toAddCommMonoidWithOne"],["propext"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["invOf_nonneg"],"typeFallback":"forall {R : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.3 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.6 : LinearOrder.{u_1} R] [inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.9 : IsStrictOrderedRing.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.3 (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.6))))] {a : R} [inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.13 : Invertible.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.3)))) a], Iff (LE.le.{u_1} R (Preorder.toLE.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.6)))))) (OfNat.ofNat.{u_1} R 0 (Zero.toOfNat0.{u_1} R (MulZeroClass.toZero.{u_1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.3)))))) (Invertible.invOf.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.3)))) a inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.13)) (LE.le.{u_1} R (Preorder.toLE.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.6)))))) (OfNat.ofNat.{u_1} R 0 (Zero.toOfNat0.{u_1} R (MulZeroClass.toZero.{u_1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Order.Invertible.826509803._hygCtx._hyg.3)))))) a)","typeFull":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  0 ≤ ⅟a ↔ 0 ≤ a","typeReadable":"∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {a : R} [inst_3 : Invertible a],\n  0 ≤ ⅟a ↔ 0 ≤ 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.QuadraticAlgebra.NormDeterminant.sym.json

@@ -0,0 +1 @@
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","inv"],["inv_pow"],["WeierstrassCurve","exists_variableChange_isShortNF"],["Mathlib","Tactic","FieldSimp","NF","eval_cons_mul_eval_cons_neg"],["instHAdd"],["Distrib","toMul"],["mul_right_inj_of_invertible"],["Mathlib","Tactic","Ring","cast_pos"],["Units","mk0"],["WeierstrassCurve","Δ_of_isShortNF"],["Mathlib","Tactic","Ring","add_congr"],["WeierstrassCurve","instSMulVariableChange"],["Ring","toAddCommGroup"],["One","toOfNat1"],["of_eq_true"],["Mathlib","Tactic","Ring","add_pf_add_zero"],["Mathlib","Tactic","Ring","neg_add"],["Nat","succ"],["Mathlib","Tactic","Ring","neg_congr"],["Field","toSemifield"],["False"],["MulAction","toSemigroupAction"],["WeierstrassCurve","a₃"],["WeierstrassCurve","a₂_of_isShortNF"],["WeierstrassCurve","a₂"],["DivInvMonoid","toInv"],["SubtractionMonoid","toSubNegZeroMonoid"],["Eq","trans"],["div_ne_zero_iff"],["Exists","intro"],["AddCancelMonoid","toAddRightCancelMonoid"],["Mathlib","Meta","NormNum","IsNatPowT","trans"],["Mathlib","Tactic","FieldSimp","NF","eval_cons"],["Mathlib","Meta","NormNum","IsInt","to_raw_eq"],["Mathlib","Tactic","LinearCombination","eq_rearrange"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["DivisionMonoid","toDivInvMonoid"],["False","elim"],["Nat","instCharZero"],["Mathlib","Tactic","Ring","one_mul"],["SubNegMonoid","toSub"],["Mathlib","Tactic","Ring","add_overlap_pf_zero"],["pow_ne_zero_iff"],["WeierstrassCurve","c₄"],["instIsCancelMulZero"],["Mathlib","Tactic","Ring","sub_pf"],["rfl"],["WeierstrassCurve","a₁_of_isShortNF"],["sub_self"],["pow_ne_zero"],["AddGroup","toAddCancelMonoid"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["Mathlib","Tactic","FieldSimp","NF","eval_mul_eval_cons_zero"],["Mathlib","Tactic","FieldSimp","eq_mul_of_eq_eq_eq_mul"],["one_ne_zero"],["Prod","snd"],["MulZeroClass","zero_mul"],["MulZeroClass","mul_zero"],["DivisionSemiring","toGroupWithZero"],["WeierstrassCurve","c₄_of_isShortNF"],["Prod"],["DivInvMonoid","toMonoid"],["Eq","refl"],["Nat","rawCast"],["one_mul"],["WeierstrassCurve","a₁"],["AddMonoid","toAddZeroClass"],["Mathlib","Meta","NormNum","IsNat","to_isInt"],["Semifield","toCommSemiring"],["Mathlib","Meta","NormNum","isNat_mul"],["Bool"],["IsDomain","to_noZeroDivisors"],["EuclideanDomain","toCommRing"],["Mathlib","Meta","NormNum","IsNatPowT","run"],["SubtractionCommMonoid","toSubtractionMonoid"],["instHDiv"],["Semigroup","toMul"],["Nat","instAddMonoidWithOne"],["Mathlib","Tactic","Ring","add_pf_add_overlap_zero"],["isReduced_of_noZeroDivisors"],["instOfNatNat"],["Nat","succ_ne_zero"],["congr"],["Mathlib","Tactic","Ring","pow_congr"],["not_true_eq_false"],["WeierstrassCurve","isCharNeTwoNF_of_isCharThreeNF"],["IsCancelMulZero","toIsLeftCancelMulZero"],["Mathlib","Tactic","Ring","mul_pow"],["Mathlib","Tactic","Ring","mul_add"],["propext"],["AddRightCancelSemigroup","toIsRightCancelAdd"],["Mathlib","Tactic","Ring","pow_zero"],["WeierstrassCurve","a₃_of_isShortNF"],["Distrib","toAdd"],["Mathlib","Tactic","FieldSimp","NF","mul_eq_eval₃"],["instIsDomain"],["Mathlib","Tactic","FieldSimp","NF","eval_cons_of_pow_eq_zero"],["IsLocalRing","toNontrivial"],["OfNat","ofNat"],["Int"],["HAdd","hAdd"],["CommRing","toRing"],["AddGroupWithOne","toAddGroup"],["Mathlib","Tactic","FieldSimp","NF","atom_eq_eval"],["AddCommGroup","toDivisionAddCommMonoid"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["congr_arg₂"],["instDecidableEqNat"],["inferInstance"],["mul_ne_zero_iff"],["dite"],["Semifield","toCommGroupWithZero"],["Mathlib","Tactic","Ring","zero_mul"],["Mathlib","Meta","NormNum","IsNat","to_raw_eq"],["Prod","mk"],["GroupWithZero","toDivInvMonoid"],["Iff","mp"],["WeierstrassCurve","VariableChange"],["WeierstrassCurve","isCharThreeNF_of_isShortNF"],["NonUnitalSemiring","toSemigroupWithZero"],["HMul","hMul"],["Int","rawCast"],["AddMonoidWithOne","toAddMonoid"],["Mathlib","Meta","NormNum","IsNat","to_eq"],["HDiv","hDiv"],["And","intro"],["Ring","toAddGroupWithOne"],["WeierstrassCurve","a₆"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["HSub","hSub"],["Mathlib","Meta","NormNum","IsInt","to_isNat"],["NonAssocRing","toNonUnitalNonAssocRing"],["instHPow"],["WeierstrassCurve","coe_Δ'"],["InvOneClass","toInv"],["MulOne","toOne"],["NonUnitalNonAssocSemiring","toDistrib"],["Neg","neg"],["Mathlib","Tactic","Ring","one_pow"],["And"],["add_zero"],["DivisionRing","toDivInvMonoid"],["invertibleOfNonzero"],["Nat","cast_zero"],["Mathlib","Meta","NormNum","instAddMonoidWithOne"],["HSMul","hSMul"],["Mathlib","Tactic","Ring","mul_pf_right"],["WeierstrassCurve","VariableChange","s"],["id"],["NegZeroClass","toZero"],["Mathlib","Meta","NormNum","isInt_pow"],["instHMul"],["WeierstrassCurve"],["NeZero","mk"],["Mathlib","Meta","NormNum","isNat_ofNat"],["Field","instIsLocalRing"],["WeierstrassCurve","VariableChange","instInv"],["div_one"],["Units","instInv"],["Mathlib","Tactic","Ring","neg_mul"],["Mathlib","Meta","NormNum","isInt_add"],["NeZero","one"],["mul_ne_zero"],["SubNegZeroMonoid","toNegZeroClass"],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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Convex.StoneSeparation.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["not_disjoint_segment_convexHull_triple"],"typeFallback":"forall {𝕜 : Type.{u_1}} {E : Type.{u_2}} [inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.4 : Field.{u_1} 𝕜] [inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.7 : LinearOrder.{u_1} 𝕜] [inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.10 : IsStrictOrderedRing.{u_1} 𝕜 (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.4))) (SemilatticeInf.toPartialOrder.{u_1} 𝕜 (Lattice.toSemilatticeInf.{u_1} 𝕜 (DistribLattice.toLattice.{u_1} 𝕜 (instDistribLatticeOfLinearOrder.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.7))))] [inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13 : AddCommGroup.{u_2} E] [inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.16 : Module.{u_1, u_2} 𝕜 E (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.4))) (AddCommGroup.toAddCommMonoid.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13)] {p : E} {q : E} {u : E} {v : E} {x : E} {y : E} {z : E}, (Membership.mem.{u_2, u_2} E (Set.{u_2} E) (Set.instMembership.{u_2} E) (segment.{u_1, u_2} 𝕜 E (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.4))) (SemilatticeInf.toPartialOrder.{u_1} 𝕜 (Lattice.toSemilatticeInf.{u_1} 𝕜 (DistribLattice.toLattice.{u_1} 𝕜 (instDistribLatticeOfLinearOrder.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.7)))) (AddCommGroup.toAddCommMonoid.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13) (SMulZeroClass.toSMul.{u_1, u_2} 𝕜 E (AddZero.toZero.{u_2} E (AddZeroClass.toAddZero.{u_2} E (AddMonoid.toAddZeroClass.{u_2} E (SubNegMonoid.toAddMonoid.{u_2} E (AddGroup.toSubNegMonoid.{u_2} E (AddCommGroup.toAddGroup.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13)))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} 𝕜 E (AddMonoid.toAddZeroClass.{u_2} E (SubNegMonoid.toAddMonoid.{u_2} E (AddGroup.toSubNegMonoid.{u_2} E (AddCommGroup.toAddGroup.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13)))) (DistribMulAction.toDistribSMul.{u_1, u_2} 𝕜 E (MonoidWithZero.toMonoid.{u_1} 𝕜 (Semiring.toMonoidWithZero.{u_1} 𝕜 (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.4))))) (SubNegMonoid.toAddMonoid.{u_2} E (AddGroup.toSubNegMonoid.{u_2} E (AddCommGroup.toAddGroup.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13))) (Module.toDistribMulAction.{u_1, u_2} 𝕜 E (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.4))) (AddCommGroup.toAddCommMonoid.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13) inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.16)))) x y) z) -> (Membership.mem.{u_2, u_2} E (Set.{u_2} E) (Set.instMembership.{u_2} E) (segment.{u_1, u_2} 𝕜 E (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.4))) (SemilatticeInf.toPartialOrder.{u_1} 𝕜 (Lattice.toSemilatticeInf.{u_1} 𝕜 (DistribLattice.toLattice.{u_1} 𝕜 (instDistribLatticeOfLinearOrder.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.7)))) (AddCommGroup.toAddCommMonoid.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13) (SMulZeroClass.toSMul.{u_1, u_2} 𝕜 E (AddZero.toZero.{u_2} E (AddZeroClass.toAddZero.{u_2} E (AddMonoid.toAddZeroClass.{u_2} E (SubNegMonoid.toAddMonoid.{u_2} E (AddGroup.toSubNegMonoid.{u_2} E (AddCommGroup.toAddGroup.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13)))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} 𝕜 E (AddMonoid.toAddZeroClass.{u_2} E (SubNegMonoid.toAddMonoid.{u_2} E (AddGroup.toSubNegMonoid.{u_2} E (AddCommGroup.toAddGroup.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13)))) (DistribMulAction.toDistribSMul.{u_1, u_2} 𝕜 E (MonoidWithZero.toMonoid.{u_1} 𝕜 (Semiring.toMonoidWithZero.{u_1} 𝕜 (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.4))))) (SubNegMonoid.toAddMonoid.{u_2} E (AddGroup.toSubNegMonoid.{u_2} E (AddCommGroup.toAddGroup.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13))) (Module.toDistribMulAction.{u_1, u_2} 𝕜 E (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.4))) (AddCommGroup.toAddCommMonoid.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13) inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.16)))) x p) u) -> (Membership.mem.{u_2, u_2} E (Set.{u_2} E) (Set.instMembership.{u_2} E) (segment.{u_1, u_2} 𝕜 E (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.4))) (SemilatticeInf.toPartialOrder.{u_1} 𝕜 (Lattice.toSemilatticeInf.{u_1} 𝕜 (DistribLattice.toLattice.{u_1} 𝕜 (instDistribLatticeOfLinearOrder.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.7)))) (AddCommGroup.toAddCommMonoid.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13) (SMulZeroClass.toSMul.{u_1, u_2} 𝕜 E (AddZero.toZero.{u_2} E (AddZeroClass.toAddZero.{u_2} E (AddMonoid.toAddZeroClass.{u_2} E (SubNegMonoid.toAddMonoid.{u_2} E (AddGroup.toSubNegMonoid.{u_2} E (AddCommGroup.toAddGroup.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13)))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} 𝕜 E (AddMonoid.toAddZeroClass.{u_2} E (SubNegMonoid.toAddMonoid.{u_2} E (AddGroup.toSubNegMonoid.{u_2} E (AddCommGroup.toAddGroup.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13)))) (DistribMulAction.toDistribSMul.{u_1, u_2} 𝕜 E (MonoidWithZero.toMonoid.{u_1} 𝕜 (Semiring.toMonoidWithZero.{u_1} 𝕜 (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.4))))) (SubNegMonoid.toAddMonoid.{u_2} E (AddGroup.toSubNegMonoid.{u_2} E (AddCommGroup.toAddGroup.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13))) (Module.toDistribMulAction.{u_1, u_2} 𝕜 E (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.4))) (AddCommGroup.toAddCommMonoid.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13) inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.16)))) y q) v) -> (Not (Disjoint.{u_2} (Set.{u_2} E) (OmegaCompletePartialOrder.toPartialOrder.{u_2} (Set.{u_2} E) (CompleteLattice.instOmegaCompletePartialOrder.{u_2} (Set.{u_2} E) (CompleteBooleanAlgebra.toCompleteLattice.{u_2} 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(AddGroup.toSubNegMonoid.{u_2} E (AddCommGroup.toAddGroup.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13))) (Module.toDistribMulAction.{u_1, u_2} 𝕜 E (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.4))) (AddCommGroup.toAddCommMonoid.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.13) inst._@.Mathlib.Analysis.Convex.StoneSeparation.4101652426._hygCtx._hyg.16)))) u v) (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (ClosureOperator.{u_2} (Set.{u_2} E) (PartialOrder.toPreorder.{u_2} (Set.{u_2} E) (OmegaCompletePartialOrder.toPartialOrder.{u_2} (Set.{u_2} E) (CompleteLattice.instOmegaCompletePartialOrder.{u_2} (Set.{u_2} E) (CompleteBooleanAlgebra.toCompleteLattice.{u_2} (Set.{u_2} E) (CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra.{u_2} (Set.{u_2} E) (Set.instCompleteAtomicBooleanAlgebra.{u_2} 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{E : Type.{u_1}} (c : Set.{u_1} (Set.{u_1} E)) (motive : (Set.Nonempty.{u_1} (Set.{u_1} E) c) -> Prop) (x._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx.115.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.126 : Set.Nonempty.{u_1} (Set.{u_1} E) c), (forall (w._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.136 : Set.{u_1} E) (h._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.137 : Membership.mem.{u_1, u_1} (Set.{u_1} E) (Set.{u_1} (Set.{u_1} E)) (Set.instMembership.{u_1} (Set.{u_1} E)) c w._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.136), motive (Exists.intro.{succ u_1} (Set.{u_1} E) (fun (x : Set.{u_1} E) => Membership.mem.{u_1, u_1} (Set.{u_1} E) (Set.{u_1} (Set.{u_1} E)) (Set.instMembership.{u_1} (Set.{u_1} E)) c x) w._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.136 h._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.137)) -> (motive 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[inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.10 : IsStrictOrderedRing.{u_1} 𝕜 (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.4))) (SemilatticeInf.toPartialOrder.{u_1} 𝕜 (Lattice.toSemilatticeInf.{u_1} 𝕜 (DistribLattice.toLattice.{u_1} 𝕜 (instDistribLatticeOfLinearOrder.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.7))))] [inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.13 : AddCommGroup.{u_2} E] [inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.16 : Module.{u_1, u_2} 𝕜 E (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.4))) (AddCommGroup.toAddCommMonoid.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.13)] 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(AddGroup.toSubNegMonoid.{u_2} E (AddCommGroup.toAddGroup.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.13)))) (DistribMulAction.toDistribSMul.{u_1, u_2} 𝕜 E (MonoidWithZero.toMonoid.{u_1} 𝕜 (Semiring.toMonoidWithZero.{u_1} 𝕜 (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.4))))) (SubNegMonoid.toAddMonoid.{u_2} E (AddGroup.toSubNegMonoid.{u_2} E (AddCommGroup.toAddGroup.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.13))) (Module.toDistribMulAction.{u_1, u_2} 𝕜 E (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.4))) (AddCommGroup.toAddCommMonoid.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.13) inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.16)))) s) -> (Convex.{u_1, u_2} 𝕜 E (DivisionSemiring.toSemiring.{u_1} 𝕜 (Semifield.toDivisionSemiring.{u_1} 𝕜 (Field.toSemifield.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.4))) (SemilatticeInf.toPartialOrder.{u_1} 𝕜 (Lattice.toSemilatticeInf.{u_1} 𝕜 (DistribLattice.toLattice.{u_1} 𝕜 (instDistribLatticeOfLinearOrder.{u_1} 𝕜 inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.7)))) (AddCommGroup.toAddCommMonoid.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.13) (SMulZeroClass.toSMul.{u_1, u_2} 𝕜 E (AddZero.toZero.{u_2} E (AddZeroClass.toAddZero.{u_2} E (AddMonoid.toAddZeroClass.{u_2} E (SubNegMonoid.toAddMonoid.{u_2} E (AddGroup.toSubNegMonoid.{u_2} E (AddCommGroup.toAddGroup.{u_2} E inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.13)))))) (DistribSMul.toSMulZeroClass.{u_1, u_2} 𝕜 E 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inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.13) inst._@.Mathlib.Analysis.Convex.StoneSeparation.852971640._hygCtx._hyg.16)))) t) -> (Disjoint.{u_2} (Set.{u_2} E) (OmegaCompletePartialOrder.toPartialOrder.{u_2} (Set.{u_2} E) (CompleteLattice.instOmegaCompletePartialOrder.{u_2} (Set.{u_2} E) (CompleteBooleanAlgebra.toCompleteLattice.{u_2} (Set.{u_2} E) (CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra.{u_2} (Set.{u_2} E) (Set.instCompleteAtomicBooleanAlgebra.{u_2} E))))) (HeytingAlgebra.toOrderBot.{u_2} (Set.{u_2} E) (Order.Frame.toHeytingAlgebra.{u_2} (Set.{u_2} E) (CompleteDistribLattice.toFrame.{u_2} (Set.{u_2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u_2} (Set.{u_2} E) (CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra.{u_2} (Set.{u_2} E) (Set.instCompleteAtomicBooleanAlgebra.{u_2} E)))))) s t) -> (Exists.{succ u_2} (Set.{u_2} E) (fun (C : Set.{u_2} E) => And (Convex.{u_1, u_2} 𝕜 E (DivisionSemiring.toSemiring.{u_1} 𝕜 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Normed.Order.Hom.Ultra.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["AddGroupSeminormClass","toSeminormedAddGroup","congr_simp"],"typeFallback":"forall {F : Type.{u_1}} {α : Type.{u_2}} [inst._@.Mathlib.Analysis.Normed.Order.Hom.Basic.3627625394._hygCtx._hyg.4 : FunLike.{succ u_1, succ u_2, 1} F α Real] [inst._@.Mathlib.Analysis.Normed.Order.Hom.Basic.3627625394._hygCtx._hyg.11 : AddGroup.{u_2} α] [inst._@.Mathlib.Analysis.Normed.Order.Hom.Basic.3627625394._hygCtx._hyg.14 : AddGroupSeminormClass.{u_1, u_2, 0} F α Real inst._@.Mathlib.Analysis.Normed.Order.Hom.Basic.3627625394._hygCtx._hyg.11 Real.instAddCommMonoid Real.partialOrder inst._@.Mathlib.Analysis.Normed.Order.Hom.Basic.3627625394._hygCtx._hyg.4] (f : F) (f_1 : F), (Eq.{succ u_1} F f f_1) -> (Eq.{succ u_2} (SeminormedAddGroup.{u_2} α) (AddGroupSeminormClass.toSeminormedAddGroup.{u_1, u_2} F α inst._@.Mathlib.Analysis.Normed.Order.Hom.Basic.3627625394._hygCtx._hyg.4 inst._@.Mathlib.Analysis.Normed.Order.Hom.Basic.3627625394._hygCtx._hyg.11 inst._@.Mathlib.Analysis.Normed.Order.Hom.Basic.3627625394._hygCtx._hyg.14 f) (AddGroupSeminormClass.toSeminormedAddGroup.{u_1, u_2} F α inst._@.Mathlib.Analysis.Normed.Order.Hom.Basic.3627625394._hygCtx._hyg.4 inst._@.Mathlib.Analysis.Normed.Order.Hom.Basic.3627625394._hygCtx._hyg.11 inst._@.Mathlib.Analysis.Normed.Order.Hom.Basic.3627625394._hygCtx._hyg.14 f_1))","typeFull":"∀ {F : Type u_1} {α : Type u_2} [inst : FunLike F α ℝ] [inst_1 : AddGroup α] [inst_2 : AddGroupSeminormClass F α ℝ]\n  (f f_1 : F), f = f_1 → AddGroupSeminormClass.toSeminormedAddGroup f = AddGroupSeminormClass.toSeminormedAddGroup f_1","typeReadable":"∀ {F : Type u_1} {α : Type u_2} [inst : FunLike F α ℝ] [inst_1 : AddGroup α] [inst_2 : AddGroupSeminormClass F α ℝ]\n  (f f_1 : F), f = f_1 → AddGroupSeminormClass.toSeminormedAddGroup f = AddGroupSeminormClass.toSeminormedAddGroup f_1","typeReferences":[["AddGroupSeminormClass"],["FunLike"],["Real"],["AddGroup"],["AddGroupSeminormClass","toSeminormedAddGroup"],["SeminormedAddGroup"],["Eq"],["Real","instAddCommMonoid"],["Real","partialOrder"]],"valueReferences":[["Eq","refl"],["AddGroupSeminormClass","toSeminormedAddGroup"],["SeminormedAddGroup"],["Eq"],["Eq","rec"]]},{"isProp":true,"kind":"theorem","name":["AddGroupSeminormClass","isUltrametricDist"],"typeFallback":"forall {F : Type.{u_1}} {α : Type.{u_2}} [inst._@.Mathlib.Analysis.Normed.Order.Hom.Ultra.484248151._hygCtx._hyg.4 : FunLike.{succ u_1, succ u_2, 1} F α Real] [inst._@.Mathlib.Analysis.Normed.Order.Hom.Ultra.484248151._hygCtx._hyg.11 : AddGroup.{u_2} α] [inst._@.Mathlib.Analysis.Normed.Order.Hom.Ultra.484248151._hygCtx._hyg.14 : AddGroupSeminormClass.{u_1, u_2, 0} F α Real inst._@.Mathlib.Analysis.Normed.Order.Hom.Ultra.484248151._hygCtx._hyg.11 Real.instAddCommMonoid Real.partialOrder 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Limits.Preserves.Shapes.Preorder.sym.json

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G).IsWellOrderContinuous","typeReferences":[["instDistribLatticeOfLinearOrder"],["CategoryTheory","Functor"],["DistribLattice","toLattice"],["Lattice","toSemilatticeInf"],["PartialOrder","toPreorder"],["CategoryTheory","Functor","IsWellOrderContinuous"],["CategoryTheory","Category"],["LinearOrder"],["Preorder","smallCategory"],["CategoryTheory","Functor","comp"],["CategoryTheory","Limits","PreservesWellOrderContinuousOfShape"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["CategoryTheory","Functor","isColimitOfIsWellOrderContinuous"],["PartialOrder","toPreorder"],["Membership","mem"],["Preorder","toLT"],["Subtype","partialOrder"],["CategoryTheory","Functor","comp"],["Set","principalSegIio"],["Set","Iio"],["DFunLike","coe"],["Set","Elem"],["CategoryTheory","Limits","IsColimit"],["RelEmbedding","instFunLike"],["CategoryTheory","Limits","isColimitOfPreserves"],["PrincipalSeg","monotone"],["instDistribLatticeOfLinearOrder"],["Nonempty","intro"],["PrincipalSeg","cocone"],["RelEmbedding"],["CategoryTheory","Limits","preservesColimitsOfShape_of_preservesWellOrderContinuousOfShape"],["CategoryTheory","Limits","PreservesColimitsOfShape","preservesColimit"],["SemilatticeInf","toPartialOrder"],["Lattice","toSemilatticeInf"],["Set"],["Preorder","smallCategory"],["Set","instMembership"],["PrincipalSeg","toRelEmbedding"],["LT","lt"],["Monotone","functor"],["DistribLattice","toLattice"],["CategoryTheory","Functor","IsWellOrderContinuous","mk"]]},{"isProp":false,"kind":"definition","name":["CategoryTheory","Limits","PreservesWellOrderContinuousOfShape","recOn"],"typeFallback":"forall 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