url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | intro J hIJ | case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.add... | case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.add... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | rw [hV'₀, Set.mem_preimage] | case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.add... | case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.add... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | apply htV₀ | case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.add... | case h.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.a... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | intro d hd | case h.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.a... | case h.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.a... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | convert mem_of_mem_nhds (ht d) using 1 | case h.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.a... | case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Ad... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | change (-_ + _) = 0 | case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Ad... | case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Ad... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | rw [neg_add_eq_sub, sub_eq_zero] | case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Ad... | case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Ad... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | symm | case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Ad... | case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Ad... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | apply StronglyMultipliable.coeff_prod_apply_eq_finset_prod hf (J := J) | case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Ad... | case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Ad... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | rw [← Set.preimage_comp, eq_comm] | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.add ⋯.prod... | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.add ⋯.prod... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | convert Set.preimage_id | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.add ⋯.prod... | case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | rw [Function.funext_iff] | case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α... | case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowe... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | intro f | case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α... | case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f✝ : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f✝
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowe... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | simp only [comp_apply, id_eq] | case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f✝ : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f✝
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ... | case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f✝ : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f✝
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f✝ : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f✝
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPo... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | change _ + (_ + f) = f | case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f✝ : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f✝
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ... | case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f✝ : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f✝
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f✝ : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f✝
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPo... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | simp_rw [← add_assoc, add_right_neg, zero_add] | case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f✝ : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f✝
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h.e'_3
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f✝ : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f✝
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPo... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | apply continuousAt_def.mp (Continuous.continuousAt (continuous_add_left _)) | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.add ⋯.prod... | case a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.add... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | rw [add_zero] | case a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.add... | case a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.add... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | exact hV | case a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Add.add... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | intro i hi | case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Ad... | case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Ad... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | apply hIJ | case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := Ad... | case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | revert hi | case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := ... | case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeri... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | contrapose | case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := ... | case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeri... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | simp only [StronglySummable.not_mem_unionOfSupportOfCoeffLe_iff] | case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := ... | case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeri... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | intro h e hed | case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := ... | case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeri... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | refine' h e (le_trans hed _) | case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := ... | case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeri... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.hasProd_of_one_add | [113, 1] | [152, 62] | apply Finset.le_sup ((Set.Finite.mem_toFinset hD).mpr hd) | case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeries σ α)
hV : V ∈ nhds ⋯.prod
V₀ : Set (MvPowerSeries σ α) := ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_4.a
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
hf : StronglySummable f
this : UniformAddGroup (MvPowerSeries σ α)
V : Set (MvPowerSeri... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.multipliable_of_one_add | [156, 1] | [157, 91] | classical exact hf.hasProd_of_one_add.multipliable | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι✝ : Type u_3
f✝ : ι✝ → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
ι : Type u_4
f : ι → MvPowerSeries σ α
hf : StronglySummable f
⊢ Multipliable fun i => 1 + f i | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι✝ : Type u_3
f✝ : ι✝ → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
ι : Type u_4
f : ι → MvPowerSeries σ α
hf : StronglySummable f
⊢ Multipliable fun i => 1 + f i
TAC... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.multipliable_of_one_add | [156, 1] | [157, 91] | exact hf.hasProd_of_one_add.multipliable | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι✝ : Type u_3
f✝ : ι✝ → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
ι : Type u_4
f : ι → MvPowerSeries σ α
hf : StronglySummable f
⊢ Multipliable fun i => 1 + f i | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
ι✝ : Type u_3
f✝ : ι✝ → MvPowerSeries σ α
inst✝² : CommRing α
inst✝¹ : UniformSpace α
inst✝ : UniformAddGroup α
ι : Type u_4
f : ι → MvPowerSeries σ α
hf : StronglySummable f
⊢ Multipliable fun i => 1 + f i
TAC... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.tprod_eq_of_one_add | [163, 1] | [166, 81] | haveI : T2Space (MvPowerSeries σ α) := t2Space σ α | σ : Type u_1
α : Type u_2
inst✝⁴ : DecidableEq σ
ι✝ : Type u_3
f✝ : ι✝ → MvPowerSeries σ α
inst✝³ : CommRing α
inst✝² : UniformSpace α
inst✝¹ : UniformAddGroup α
inst✝ : T2Space α
ι : Type u_4
f : ι → MvPowerSeries σ α
hf : StronglySummable f
⊢ ∏' (i : ι), (1 + f i) = tsum (partialProduct f) | σ : Type u_1
α : Type u_2
inst✝⁴ : DecidableEq σ
ι✝ : Type u_3
f✝ : ι✝ → MvPowerSeries σ α
inst✝³ : CommRing α
inst✝² : UniformSpace α
inst✝¹ : UniformAddGroup α
inst✝ : T2Space α
ι : Type u_4
f : ι → MvPowerSeries σ α
hf : StronglySummable f
this : T2Space (MvPowerSeries σ α)
⊢ ∏' (i : ι), (1 + f i) = tsum (partialPro... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝⁴ : DecidableEq σ
ι✝ : Type u_3
f✝ : ι✝ → MvPowerSeries σ α
inst✝³ : CommRing α
inst✝² : UniformSpace α
inst✝¹ : UniformAddGroup α
inst✝ : T2Space α
ι : Type u_4
f : ι → MvPowerSeries σ α
hf : StronglySummable f
⊢ ∏' (i : ι), (1... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Topology.lean | MvPowerSeries.StronglySummable.tprod_eq_of_one_add | [163, 1] | [166, 81] | rw [hf.hasProd_of_one_add.tprod_eq, StronglyMultipliable.prod_eq, sum_eq_tsum] | σ : Type u_1
α : Type u_2
inst✝⁴ : DecidableEq σ
ι✝ : Type u_3
f✝ : ι✝ → MvPowerSeries σ α
inst✝³ : CommRing α
inst✝² : UniformSpace α
inst✝¹ : UniformAddGroup α
inst✝ : T2Space α
ι : Type u_4
f : ι → MvPowerSeries σ α
hf : StronglySummable f
this : T2Space (MvPowerSeries σ α)
⊢ ∏' (i : ι), (1 + f i) = tsum (partialPro... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝⁴ : DecidableEq σ
ι✝ : Type u_3
f✝ : ι✝ → MvPowerSeries σ α
inst✝³ : CommRing α
inst✝² : UniformSpace α
inst✝¹ : UniformAddGroup α
inst✝ : T2Space α
ι : Type u_4
f : ι → MvPowerSeries σ α
hf : StronglySummable f
this : T2Space (... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | have hq :∀ x ∈ Finset.filter
(fun x : (ℕ × ℕ) × ℕ × ℕ => x.fst.fst + x.snd.fst = u ∧ x.fst.snd + x.snd.snd = v)
(Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.fst ∈ Finset.antidiagonal m := by
intro x; simp; intro h'; simp [h'] | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
⊢ (Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)).sum
g =
... | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
⊢ (Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Fins... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [← Finset.sum_fiberwise_of_maps_to hq] | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.... | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | apply Finset.sum_congr rfl | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.... | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rintro ⟨i, j⟩ hij | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.... | case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp only [Finset.mem_antidiagonal] at hij | case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [Finset.sum_filter] | case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [Finset.sum_filter] | case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp_rw [← ite_and] | case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | intro x | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
⊢ ∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.1 ∈ F... | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
x : (ℕ × ℕ) × ℕ × ℕ
⊢ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagon... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
⊢ ∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
x : (ℕ × ℕ) × ℕ × ℕ
⊢ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagon... | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
x : (ℕ × ℕ) × ℕ × ℕ
⊢ x.1.1 + x.1.2 = m → x.2.1 + x.2.2 = n → x.1.1 + x.2.1 = u → x.1.2 + x.2.2 = v → x.1.1 + x.1.2 = m | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
x : (ℕ × ℕ) × ℕ × ℕ
⊢ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | intro h' | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
x : (ℕ × ℕ) × ℕ × ℕ
⊢ x.1.1 + x.1.2 = m → x.2.1 + x.2.2 = n → x.1.1 + x.2.1 = u → x.1.2 + x.2.2 = v → x.1.1 + x.1.2 = m | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
x : (ℕ × ℕ) × ℕ × ℕ
h' : x.1.1 + x.1.2 = m
⊢ x.2.1 + x.2.2 = n → x.1.1 + x.2.1 = u → x.1.2 + x.2.2 = v → x.1.1 + x.1.2 = m | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
x : (ℕ × ℕ) × ℕ × ℕ
⊢ x.1.1 + x.1.2 = m → x.2.1 + x.2.2 = n → x.1.1 + x... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp [h'] | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
x : (ℕ × ℕ) × ℕ × ℕ
h' : x.1.1 + x.1.2 = m
⊢ x.2.1 + x.2.2 = n → x.1.1 + x.2.1 = u → x.1.2 + x.2.2 = v → x.1.1 + x.1.2 = m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
x : (ℕ × ℕ) × ℕ × ℕ
h' : x.1.1 + x.1.2 = m
⊢ x.2.1 + x.2.2 = n → x.1.1 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [Finset.sum_congr rfl fun x _ => hf' x, ← Finset.sum_mul] | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.... | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | by_cases hij' : i ≤ u ∧ j ≤ v | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.... | case pos
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | conv_rhs => rw [← one_mul (f ⟨i, j⟩)] | case pos
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n... | case pos
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | apply congr_arg₂ _ _ rfl | case pos
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n... | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [Finset.sum_eq_single (⟨⟨i, j⟩, ⟨u - i, v - j⟩⟩ : (ℕ × ℕ) × ℕ × ℕ)] | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.... | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp only [Nat.add_sub_of_le hij'.1, Nat.add_sub_of_le hij'.2, eq_self_iff_true, and_self_iff,
if_true] | α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n),
x.... | case h₀
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rintro ⟨⟨x, y⟩, ⟨z, t⟩⟩ hb hb' | case h₀
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | case h₀.mk.mk.mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidi... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₀
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [if_neg] | case h₀.mk.mk.mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidi... | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₀.mk.mk.mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | intro hb'' | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp only [Finset.mem_product, Finset.mem_antidiagonal] at hb | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp only [ne_eq, Prod.mk.injEq, not_and, and_imp] at hb' | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp only [Prod.mk.inj_iff] at hb'' | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | specialize hb' hb''.2.1 hb''.2.2 | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [hb''.2.1, hb''.2.2] at hb | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | apply hb' | case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.an... | case h₀.mk.mk.mk.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₀.mk.mk.mk.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | apply Nat.add_left_cancel | case h₀.mk.mk.mk.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.... | case h₀.mk.mk.mk.hnc.a.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finse... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₀.mk.mk.mk.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [Nat.add_sub_of_le hij'.1, ← hb''.2.1, hb''.1.1] | case h₀.mk.mk.mk.hnc.a.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finse... | case h₀.mk.mk.mk.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₀.mk.mk.mk.hnc.a.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | apply Nat.add_left_cancel | case h₀.mk.mk.mk.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.... | case h₀.mk.mk.mk.hnc.a.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finse... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₀.mk.mk.mk.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [Nat.add_sub_of_le hij'.2, ← hb''.2.2, hb''.1.2] | case h₀.mk.mk.mk.hnc.a.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finse... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h₀.mk.mk.mk.hnc.a.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | intro hb | case h₁
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | case h₁
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [if_neg] | case h₁
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagona... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | intro hb' | case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagona... | case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagona... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | apply hb | case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagona... | case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagona... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp only [eq_self_iff_true, and_true_iff] at hb' | case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagona... | case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagona... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp only [Finset.mem_product, Finset.mem_antidiagonal] | case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagona... | case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagona... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | apply And.intro hij | case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagona... | case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagona... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | apply Nat.add_left_cancel | case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagona... | case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiago... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.hnc
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [h, ← hij] | case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiago... | case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiago... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | conv_rhs => rw [← hb'.1, ← hb'.2] | case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiago... | case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiago... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp only [← add_assoc, add_left_inj] | case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiago... | case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiago... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp only [add_assoc, add_right_inj] | case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiago... | case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiago... | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | apply add_comm | case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiago... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h₁.hnc.a
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp only [not_and_or, not_le] at hij' | case neg
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n... | case neg
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [hf ⟨i, j⟩ hij', MulZeroClass.mul_zero] | case neg
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | intro x | case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | split_ifs with hx | case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n)... | case pos
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | simp only [one_mul, hgf] | case pos
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n... | case pos
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [hx.2] | case pos
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | rewriting_4_fold_sums | [47, 1] | [101, 33] | rw [MulZeroClass.zero_mul] | case neg
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2 + x.2.2 = v) (Finset.antidiagonal m ×ˢ Finset.antidiagonal n... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝ : CommSemiring α
m n u v : ℕ
h : m + n = u + v
f : ℕ × ℕ → α
g : (ℕ × ℕ) × ℕ × ℕ → α
hgf : g = fun x => f (x.1.1, x.1.2)
hf : ∀ (x : ℕ × ℕ), u < x.1 ∨ v < x.2 → f x = 0
hq :
∀ x ∈ Finset.filter (fun x => x.1.1 + x.2.1 = u ∧ x.1.2... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | simp only [Finset.sum_sigma'] | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
⊢ (∑ x ∈ antidiagonal n,
match x with
| (k, l) =>
∑ x ∈ antidiagonal k,
match x with
| (a, b) =>
∑ x ∈ antidiagonal l,
match x with
| (c, d) => f (a, b, c, d)) =
∑ x ∈ ant... | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
⊢ ∑ x ∈ (antidiagonal n).sigma fun a => (antidiagonal a.1).sigma fun a_1 => antidiagonal a.2,
f (x.snd.fst.1, x.snd.fst.2, x.snd.snd.1, x.snd.snd.2) =
∑ x ∈ (antidiagonal n).sigma fun a => (antidiagonal a.1).sigma fun a_1 => antidiagonal a.2,
... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
⊢ (∑ x ∈ antidiagonal n,
match x with
| (k, l) =>
∑ x ∈ antidiagonal k,
match x with
| (a, b) =>
∑ x ∈ antidiagonal l,
match x w... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | set φ : ((_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ) → ((_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ) :=
fun ⟨⟨_, _⟩, ⟨⟨a, b⟩, ⟨c, d⟩⟩⟩ ↦ ⟨⟨a+c, b+ d⟩, ⟨⟨a, c⟩, ⟨b, d⟩⟩⟩ | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
⊢ ∑ x ∈ (antidiagonal n).sigma fun a => (antidiagonal a.1).sigma fun a_1 => antidiagonal a.2,
f (x.snd.fst.1, x.snd.fst.2, x.snd.snd.1, x.snd.snd.2) =
∑ x ∈ (antidiagonal n).sigma fun a => (antidiagonal a.1).sigma fun a_1 => antidiagonal a.2,
... | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
⊢ ∑ x ∈ (antidiagonal n).sigma fun a => (antidiagonal a.1).sigma fun a_1 =>... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
⊢ ∑ x ∈ (antidiagonal n).sigma fun a => (antidiagonal a.1).sigma fun a_1 => antidiagonal a.2,
f (x.snd.fst.1, x.snd.fst.2, x.snd.snd.1, x.snd.snd.2) =
∑ x ∈ (antidiagonal n).sigma fun ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | suffices hφ : _ by
suffices hφ' : _ by
apply Finset.sum_bij' (fun m _ => φ m) (fun m _ => φ m) hφ hφ hφ' hφ'
rintro ⟨⟨k, l⟩, ⟨⟨a, b⟩, ⟨c, d⟩⟩⟩ H
simp only [mem_sigma, mem_antidiagonal] at H ⊢
rintro ⟨⟨k, l⟩, ⟨⟨a, b⟩, ⟨c, d⟩⟩⟩ H
simp only [mem_sigma, mem_antidiagonal] at H ⊢
simp only [Sigma.mk.inj_i... | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
⊢ ∑ x ∈ (antidiagonal n).sigma fun a => (antidiagonal a.1).sigma fun a_1 =>... | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
⊢ ∀ (a : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ)
(ha : a ∈ (antidiagonal n).... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
⊢ ∑ x ∈ (antid... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | rintro ⟨⟨k, l⟩, ⟨⟨a, b⟩, ⟨c, d⟩⟩⟩ H | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
⊢ ∀ (a : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ)
(ha : a ∈ (antidiagonal n).... | case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
k l a b c d : ℕ
H : ⟨(k, l), ⟨(a, b), (c, d)⟩⟩ ∈ (antid... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
⊢ ∀ (a : (_ : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | simp only [mem_sigma, mem_antidiagonal, and_self, and_true] at H ⊢ | case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
k l a b c d : ℕ
H : ⟨(k, l), ⟨(a, b), (c, d)⟩⟩ ∈ (antid... | case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
k l a b c d : ℕ
H : k + l = n ∧ a + b = k ∧ c + d = l
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b,... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | rw [← H.1, ← H.2.1, ← H.2.2] | case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
k l a b c d : ℕ
H : k + l = n ∧ a + b = k ∧ c + d = l
⊢... | case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
k l a b c d : ℕ
H : k + l = n ∧ a + b = k ∧ c + d = l
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b,... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | abel | case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
k l a b c d : ℕ
H : k + l = n ∧ a + b = k ∧ c + d = l
⊢... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b,... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | suffices hφ' : _ by
apply Finset.sum_bij' (fun m _ => φ m) (fun m _ => φ m) hφ hφ hφ' hφ'
rintro ⟨⟨k, l⟩, ⟨⟨a, b⟩, ⟨c, d⟩⟩⟩ H
simp only [mem_sigma, mem_antidiagonal] at H ⊢ | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ : ?m.15077
⊢ ∑ x ∈ (antidiagonal n).sigma fun a => (antidiagonal a.1).si... | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ :
∀ (a : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ)
(ha : a ∈ (antidiagona... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ : ?m.15077
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | rintro ⟨⟨k, l⟩, ⟨⟨a, b⟩, ⟨c, d⟩⟩⟩ H | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ :
∀ (a : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ)
(ha : a ∈ (antidiagona... | case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ :
∀ (a : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ)
(h... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ :
∀ (a : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | simp only [mem_sigma, mem_antidiagonal] at H ⊢ | case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ :
∀ (a : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ)
(h... | case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ :
∀ (a : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ)
(h... | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b,... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | simp only [Sigma.mk.inj_iff, Prod.mk.injEq, heq_eq_eq, and_true, φ, H.2.1, H.2.2] | case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ :
∀ (a : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ)
(h... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b,... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | apply Finset.sum_bij' (fun m _ => φ m) (fun m _ => φ m) hφ hφ hφ' hφ' | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ : ?m.15077
hφ' : ?m.15083
⊢ ∑ x ∈ (antidiagonal n).sigma fun a => (antid... | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ :
∀ (a : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ)
(ha : a ∈ (antidiagona... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ : ?m.15077
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | rintro ⟨⟨k, l⟩, ⟨⟨a, b⟩, ⟨c, d⟩⟩⟩ H | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ :
∀ (a : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ)
(ha : a ∈ (antidiagona... | case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ :
∀ (a : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ)
(h... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ :
∀ (a : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw' | [114, 1] | [135, 37] | simp only [mem_sigma, mem_antidiagonal] at H ⊢ | case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b, d)⟩⟩
hφ :
∀ (a : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ)
(h... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mk.mk.mk.mk.mk
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ → (_ : ℕ × ℕ) × (_ : ℕ × ℕ) × ℕ × ℕ :=
fun x =>
match x with
| ⟨(fst, snd), ⟨(a, b), (c, d)⟩⟩ => ⟨(a + c, b + d), ⟨(a, c), (b,... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw | [139, 1] | [185, 63] | rw [Finset.sum_sigma', Finset.sum_sigma', Finset.sum_sigma', Finset.sum_sigma'] | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
⊢ ∑ k ∈ range (n + 1), ∑ a ∈ range (k + 1), ∑ c ∈ range (n - k + 1), f (a, k - a, c, n - k - c) =
∑ l ∈ range (n + 1), ∑ a ∈ range (l + 1), ∑ b ∈ range (n - l + 1), f (a, b, l - a, n - l - b) | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
⊢ ∑ x ∈ ((range (n + 1)).sigma fun k => range (k + 1)).sigma fun x => range (n - x.fst + 1),
f (x.fst.snd, x.fst.fst - x.fst.snd, x.snd, n - x.fst.fst - x.snd) =
∑ x ∈ ((range (n + 1)).sigma fun l => range (l + 1)).sigma fun x => range (n - x.fs... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
⊢ ∑ k ∈ range (n + 1), ∑ a ∈ range (k + 1), ∑ c ∈ range (n - k + 1), f (a, k - a, c, n - k - c) =
∑ l ∈ range (n + 1), ∑ a ∈ range (l + 1), ∑ b ∈ range (n - l + 1), f (a, b, l - a, n - l - b... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw | [139, 1] | [185, 63] | let φ : (Σ (_ : Σ (_ : ℕ), ℕ), ℕ) → (Σ (_ : Σ (_ : ℕ), ℕ), ℕ) :=
fun ⟨⟨k, a⟩, c⟩ => ⟨⟨a + c, a⟩, k - a⟩ | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
⊢ ∑ x ∈ ((range (n + 1)).sigma fun k => range (k + 1)).sigma fun x => range (n - x.fst + 1),
f (x.fst.snd, x.fst.fst - x.fst.snd, x.snd, n - x.fst.fst - x.snd) =
∑ x ∈ ((range (n + 1)).sigma fun l => range (l + 1)).sigma fun x => range (n - x.fs... | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : (_ : ℕ) × ℕ) × ℕ → (_ : (_ : ℕ) × ℕ) × ℕ :=
fun x =>
match x with
| ⟨⟨k, a⟩, c⟩ => ⟨⟨a + c, a⟩, k - a⟩
⊢ ∑ x ∈ ((range (n + 1)).sigma fun k => range (k + 1)).sigma fun x => range (n - x.fst + 1),
f (x.fst.snd, x.fst.fst - x.fst.sn... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
⊢ ∑ x ∈ ((range (n + 1)).sigma fun k => range (k + 1)).sigma fun x => range (n - x.fst + 1),
f (x.fst.snd, x.fst.fst - x.fst.snd, x.snd, n - x.fst.fst - x.snd) =
∑ x ∈ ((range (n + 1))... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw | [139, 1] | [185, 63] | have h2 : ∀ (a : (_ : (_ : ℕ) × ℕ) × ℕ) (ha : a ∈ Finset.sigma (Finset.sigma (range (n + 1))
fun k => range (k + 1)) fun x => range (n - x.fst + 1)),
(fun m _ => φ m) ((fun m _ => φ m) a ha) ((fun m _ => φ m) a ha ∈
Finset.sigma (Finset.sigma (range (n + 1)) fun k => range (k + 1))
fun x => range ... | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : (_ : ℕ) × ℕ) × ℕ → (_ : (_ : ℕ) × ℕ) × ℕ :=
fun x =>
match x with
| ⟨⟨k, a⟩, c⟩ => ⟨⟨a + c, a⟩, k - a⟩
h1 :
∀ (a : (_ : (_ : ℕ) × ℕ) × ℕ)
(ha : a ∈ ((range (n + 1)).sigma fun l => range (l + 1)).sigma fun x => range (n - x.fst + 1... | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : (_ : ℕ) × ℕ) × ℕ → (_ : (_ : ℕ) × ℕ) × ℕ :=
fun x =>
match x with
| ⟨⟨k, a⟩, c⟩ => ⟨⟨a + c, a⟩, k - a⟩
h1 :
∀ (a : (_ : (_ : ℕ) × ℕ) × ℕ)
(ha : a ∈ ((range (n + 1)).sigma fun l => range (l + 1)).sigma fun x => range (n - x.fst + 1... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : (_ : ℕ) × ℕ) × ℕ → (_ : (_ : ℕ) × ℕ) × ℕ :=
fun x =>
match x with
| ⟨⟨k, a⟩, c⟩ => ⟨⟨a + c, a⟩, k - a⟩
h1 :
∀ (a : (_ : (_ : ℕ) × ℕ) × ℕ)
(ha : a ∈ ((range (n + 1)).sigm... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/BasicLemmas.lean | Finset.sum_4_rw | [139, 1] | [185, 63] | refine Finset.sum_bij' (fun m _ => φ m) (fun m _ => φ m) h1 h1 h2 h2 ?_ | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : (_ : ℕ) × ℕ) × ℕ → (_ : (_ : ℕ) × ℕ) × ℕ :=
fun x =>
match x with
| ⟨⟨k, a⟩, c⟩ => ⟨⟨a + c, a⟩, k - a⟩
h1 :
∀ (a : (_ : (_ : ℕ) × ℕ) × ℕ)
(ha : a ∈ ((range (n + 1)).sigma fun l => range (l + 1)).sigma fun x => range (n - x.fst + 1... | α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : (_ : ℕ) × ℕ) × ℕ → (_ : (_ : ℕ) × ℕ) × ℕ :=
fun x =>
match x with
| ⟨⟨k, a⟩, c⟩ => ⟨⟨a + c, a⟩, k - a⟩
h1 :
∀ (a : (_ : (_ : ℕ) × ℕ) × ℕ)
(ha : a ∈ ((range (n + 1)).sigma fun l => range (l + 1)).sigma fun x => range (n - x.fst + 1... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : AddCommMonoid α
f : ℕ × ℕ × ℕ × ℕ → α
n : ℕ
φ : (_ : (_ : ℕ) × ℕ) × ℕ → (_ : (_ : ℕ) × ℕ) × ℕ :=
fun x =>
match x with
| ⟨⟨k, a⟩, c⟩ => ⟨⟨a + c, a⟩, k - a⟩
h1 :
∀ (a : (_ : (_ : ℕ) × ℕ) × ℕ)
(ha : a ∈ ((range (n + 1)).sigm... |
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