Datasets:
internlm
/
Lean-Github

Dataset card Data Studio Files Community
1
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stringclasses
147 values
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6
2.09M
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.v_discr_of_v_ai
[443, 1]
[453, 14]
apply_rules [val_add_ge_of_ge, val_sub_ge_of_ge] <;> . simp elinarith
R : Type u inst✝ : CommRing R inst : IsDomain R p : R q : ℕ valp : SurjVal p e : ValidModel R hq : q > 1 h1 : v valp e.a1 ≥ 1 h2 : v valp e.a2 = 1 h3 : v valp e.a3 ≥ ↑q h4 : v valp e.a4 ≥ ↑q + 1 h6 : v valp e.a6 ≥ 2 * ↑q h2' : v valp (Model.b2 e.toModel) ≥ 1 h4' : v valp (Model.b4 e.toModel) ≥ ↑q + 1 h6' : v valp (Model.b6 e.toModel) ≥ 2 * ↑q h8' : v valp (Model.b8 e.toModel) ≥ 2 * ↑q + 1 ⊢ v valp (Model.discr e.toModel) ≥ 2 * ↑q + 3
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.v_discr_of_v_ai
[443, 1]
[453, 14]
simp
case hb R : Type u inst✝ : CommRing R inst : IsDomain R p : R q : ℕ valp : SurjVal p e : ValidModel R hq : q > 1 h1 : v valp e.a1 ≥ 1 h2 : v valp e.a2 = 1 h3 : v valp e.a3 ≥ ↑q h4 : v valp e.a4 ≥ ↑q + 1 h6 : v valp e.a6 ≥ 2 * ↑q h2' : v valp (Model.b2 e.toModel) ≥ 1 h4' : v valp (Model.b4 e.toModel) ≥ ↑q + 1 h6' : v valp (Model.b6 e.toModel) ≥ 2 * ↑q h8' : v valp (Model.b8 e.toModel) ≥ 2 * ↑q + 1 h2_symm : 1 = v valp e.a2 ⊢ 2 * ↑q + 3 ≤ v valp (9 * Model.b2 e.toModel * Model.b4 e.toModel * Model.b6 e.toModel)
case hb R : Type u inst✝ : CommRing R inst : IsDomain R p : R q : ℕ valp : SurjVal p e : ValidModel R hq : q > 1 h1 : v valp e.a1 ≥ 1 h2 : v valp e.a2 = 1 h3 : v valp e.a3 ≥ ↑q h4 : v valp e.a4 ≥ ↑q + 1 h6 : v valp e.a6 ≥ 2 * ↑q h2' : v valp (Model.b2 e.toModel) ≥ 1 h4' : v valp (Model.b4 e.toModel) ≥ ↑q + 1 h6' : v valp (Model.b6 e.toModel) ≥ 2 * ↑q h8' : v valp (Model.b8 e.toModel) ≥ 2 * ↑q + 1 h2_symm : 1 = v valp e.a2 ⊢ 2 * ↑q + 3 ≤ v valp 9 + v valp (Model.b2 e.toModel) + v valp (Model.b4 e.toModel) + v valp (Model.b6 e.toModel)
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.v_discr_of_v_ai
[443, 1]
[453, 14]
elinarith
case hb R : Type u inst✝ : CommRing R inst : IsDomain R p : R q : ℕ valp : SurjVal p e : ValidModel R hq : q > 1 h1 : v valp e.a1 ≥ 1 h2 : v valp e.a2 = 1 h3 : v valp e.a3 ≥ ↑q h4 : v valp e.a4 ≥ ↑q + 1 h6 : v valp e.a6 ≥ 2 * ↑q h2' : v valp (Model.b2 e.toModel) ≥ 1 h4' : v valp (Model.b4 e.toModel) ≥ ↑q + 1 h6' : v valp (Model.b6 e.toModel) ≥ 2 * ↑q h8' : v valp (Model.b8 e.toModel) ≥ 2 * ↑q + 1 h2_symm : 1 = v valp e.a2 ⊢ 2 * ↑q + 3 ≤ v valp 9 + v valp (Model.b2 e.toModel) + v valp (Model.b4 e.toModel) + v valp (Model.b6 e.toModel)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.small_char_div_12
[507, 1]
[518, 45]
cases hp with | inl p2 => rw [(show (12 : R) = 2 * 6 by norm_num)] apply val_mul_ge_of_left_ge rw [←p2] exact le_of_eq (valp.v_uniformizer).symm | inr p3 => rw [(show (12 : R) = 3 * 4 by norm_num)] apply val_mul_ge_of_left_ge rw [←p3] exact le_of_eq (valp.v_uniformizer).symm
R : Type u inst✝ : CommRing R inst : IsDomain R p : R hp : p = 2 ∨ p = 3 valp : SurjVal p ⊢ v valp 12 ≥ 1
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.small_char_div_12
[507, 1]
[518, 45]
rw [(show (12 : R) = 2 * 6 by norm_num)]
case inl R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p2 : p = 2 ⊢ v valp 12 ≥ 1
case inl R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p2 : p = 2 ⊢ v valp (2 * 6) ≥ 1
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.small_char_div_12
[507, 1]
[518, 45]
apply val_mul_ge_of_left_ge
case inl R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p2 : p = 2 ⊢ v valp (2 * 6) ≥ 1
case inl.ha R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p2 : p = 2 ⊢ 1 ≤ v valp 2
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.small_char_div_12
[507, 1]
[518, 45]
rw [←p2]
case inl.ha R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p2 : p = 2 ⊢ 1 ≤ v valp 2
case inl.ha R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p2 : p = 2 ⊢ 1 ≤ v valp p
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.small_char_div_12
[507, 1]
[518, 45]
exact le_of_eq (valp.v_uniformizer).symm
case inl.ha R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p2 : p = 2 ⊢ 1 ≤ v valp p
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.small_char_div_12
[507, 1]
[518, 45]
norm_num
R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p2 : p = 2 ⊢ 12 = 2 * 6
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.small_char_div_12
[507, 1]
[518, 45]
rw [(show (12 : R) = 3 * 4 by norm_num)]
case inr R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p3 : p = 3 ⊢ v valp 12 ≥ 1
case inr R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p3 : p = 3 ⊢ v valp (3 * 4) ≥ 1
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.small_char_div_12
[507, 1]
[518, 45]
apply val_mul_ge_of_left_ge
case inr R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p3 : p = 3 ⊢ v valp (3 * 4) ≥ 1
case inr.ha R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p3 : p = 3 ⊢ 1 ≤ v valp 3
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.small_char_div_12
[507, 1]
[518, 45]
rw [←p3]
case inr.ha R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p3 : p = 3 ⊢ 1 ≤ v valp 3
case inr.ha R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p3 : p = 3 ⊢ 1 ≤ v valp p
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.small_char_div_12
[507, 1]
[518, 45]
exact le_of_eq (valp.v_uniformizer).symm
case inr.ha R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p3 : p = 3 ⊢ 1 ≤ v valp p
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.small_char_div_12
[507, 1]
[518, 45]
norm_num
R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p p3 : p = 3 ⊢ 12 = 3 * 4
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.v_rst_b2_of_small_char
[520, 1]
[526, 39]
simp only [rst_iso]
R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p e : ValidModel R r s t : R h_b2 : v valp (Model.b2 e.toModel) ≥ 1 h_p : v valp 12 ≥ 1 ⊢ v valp (Model.b2 (rst_iso r s t e).toModel) ≥ 1
R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p e : ValidModel R r s t : R h_b2 : v valp (Model.b2 e.toModel) ≥ 1 h_p : v valp 12 ≥ 1 ⊢ v valp (Model.b2 (Model.rst_iso r s t e.toModel)) ≥ 1
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.v_rst_b2_of_small_char
[520, 1]
[526, 39]
rw [Model.rst_b2]
R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p e : ValidModel R r s t : R h_b2 : v valp (Model.b2 e.toModel) ≥ 1 h_p : v valp 12 ≥ 1 ⊢ v valp (Model.b2 (Model.rst_iso r s t e.toModel)) ≥ 1
R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p e : ValidModel R r s t : R h_b2 : v valp (Model.b2 e.toModel) ≥ 1 h_p : v valp 12 ≥ 1 ⊢ v valp (Model.b2 e.toModel + 12 * r) ≥ 1
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.v_rst_b2_of_small_char
[520, 1]
[526, 39]
apply val_add_ge_of_ge valp h_b2
R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p e : ValidModel R r s t : R h_b2 : v valp (Model.b2 e.toModel) ≥ 1 h_p : v valp 12 ≥ 1 ⊢ v valp (Model.b2 e.toModel + 12 * r) ≥ 1
R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p e : ValidModel R r s t : R h_b2 : v valp (Model.b2 e.toModel) ≥ 1 h_p : v valp 12 ≥ 1 ⊢ 1 ≤ v valp (12 * r)
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/LocalEC.lean
ValidModel.v_rst_b2_of_small_char
[520, 1]
[526, 39]
exact val_mul_ge_of_left_ge valp h_p
R : Type u inst✝ : CommRing R inst : IsDomain R p : R valp : SurjVal p e : ValidModel R r s t : R h_b2 : v valp (Model.b2 e.toModel) ≥ 1 h_p : v valp 12 ≥ 1 ⊢ 1 ≤ v valp (12 * r)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Data/Nat/Enat.lean
ENat.mul_infty
[687, 1]
[693, 21]
simp
case top R : Type u inst✝ : CommRing R x : R I : Ideal R J : Ideal (R ⧸ I) ⊢ ⊤ * ⊤ = if ⊤ = 0 then 0 else ⊤
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Data/Nat/Enat.lean
ENat.mul_infty
[687, 1]
[693, 21]
cases n
case nat R : Type u inst✝ : CommRing R x : R I : Ideal R J : Ideal (R ⧸ I) n : ℕ ⊢ ↑n * ⊤ = if ↑n = 0 then 0 else ⊤
case nat.zero R : Type u inst✝ : CommRing R x : R I : Ideal R J : Ideal (R ⧸ I) ⊢ ↑Nat.zero * ⊤ = if ↑Nat.zero = 0 then 0 else ⊤ case nat.succ R : Type u inst✝ : CommRing R x : R I : Ideal R J : Ideal (R ⧸ I) n✝ : ℕ ⊢ ↑(Nat.succ n✝) * ⊤ = if ↑(Nat.succ n✝) = 0 then 0 else ⊤
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Data/Nat/Enat.lean
ENat.mul_infty
[687, 1]
[693, 21]
simp
case nat.zero R : Type u inst✝ : CommRing R x : R I : Ideal R J : Ideal (R ⧸ I) ⊢ ↑Nat.zero * ⊤ = if ↑Nat.zero = 0 then 0 else ⊤
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Data/Nat/Enat.lean
ENat.mul_infty
[687, 1]
[693, 21]
simp [add_mul]
case nat.succ R : Type u inst✝ : CommRing R x : R I : Ideal R J : Ideal (R ⧸ I) n✝ : ℕ ⊢ ↑(Nat.succ n✝) * ⊤ = if ↑(Nat.succ n✝) = 0 then 0 else ⊤
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Data/Nat/Enat.lean
ENat.infty_mul
[695, 1]
[701, 21]
simp
case top R : Type u inst✝ : CommRing R x : R I : Ideal R J : Ideal (R ⧸ I) ⊢ ⊤ * ⊤ = if ⊤ = 0 then 0 else ⊤
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Data/Nat/Enat.lean
ENat.infty_mul
[695, 1]
[701, 21]
cases n
case nat R : Type u inst✝ : CommRing R x : R I : Ideal R J : Ideal (R ⧸ I) n : ℕ ⊢ ⊤ * ↑n = if ↑n = 0 then 0 else ⊤
case nat.zero R : Type u inst✝ : CommRing R x : R I : Ideal R J : Ideal (R ⧸ I) ⊢ ⊤ * ↑Nat.zero = if ↑Nat.zero = 0 then 0 else ⊤ case nat.succ R : Type u inst✝ : CommRing R x : R I : Ideal R J : Ideal (R ⧸ I) n✝ : ℕ ⊢ ⊤ * ↑(Nat.succ n✝) = if ↑(Nat.succ n✝) = 0 then 0 else ⊤
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Data/Nat/Enat.lean
ENat.infty_mul
[695, 1]
[701, 21]
simp
case nat.zero R : Type u inst✝ : CommRing R x : R I : Ideal R J : Ideal (R ⧸ I) ⊢ ⊤ * ↑Nat.zero = if ↑Nat.zero = 0 then 0 else ⊤
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Data/Nat/Enat.lean
ENat.infty_mul
[695, 1]
[701, 21]
simp [mul_add]
case nat.succ R : Type u inst✝ : CommRing R x : R I : Ideal R J : Ideal (R ⧸ I) n✝ : ℕ ⊢ ⊤ * ↑(Nat.succ n✝) = if ↑(Nat.succ n✝) = 0 then 0 else ⊤
no goals
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Termination/Init/Prelude.lean
usize_size_eq
[1888, 1]
[1892, 40]
decide
⊢ Eq (hPow 2 32) 4294967296
no goals
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Termination/Init/Prelude.lean
usize_size_eq
[1888, 1]
[1892, 40]
decide
⊢ Eq (hPow 2 64) 18446744073709551616
no goals
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Termination/Init/Prelude.lean
isValidChar_UInt32
[1973, 1]
[1976, 48]
decide
n : Nat h✝ : Nat.isValidChar n h : LT.lt n 55296 ⊢ LT.lt 55296 UInt32.size
no goals
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Termination/Init/Prelude.lean
isValidChar_UInt32
[1973, 1]
[1976, 48]
decide
n : Nat h✝ : Nat.isValidChar n left✝ : LT.lt 57343 n h : LT.lt n 1114112 ⊢ LT.lt 1114112 UInt32.size
no goals
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Debug/AddComm.lean
add_comm
[1, 1]
[7, 15]
have : Nat.succ (n + m) = Nat.succ (m + n) := by apply congrArg; apply Nat.add_comm
n m : Nat ⊢ n + (m + 1) = m + 1 + n
n m : Nat this : Nat.succ (n + m) = Nat.succ (m + n) ⊢ n + (m + 1) = m + 1 + n
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Debug/AddComm.lean
add_comm
[1, 1]
[7, 15]
rw [Nat.succ_add m n]
n m : Nat this : Nat.succ (n + m) = Nat.succ (m + n) ⊢ n + (m + 1) = m + 1 + n
n m : Nat this : Nat.succ (n + m) = Nat.succ (m + n) ⊢ n + (m + 1) = Nat.succ (m + n)
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Debug/AddComm.lean
add_comm
[1, 1]
[7, 15]
apply this
n m : Nat this : Nat.succ (n + m) = Nat.succ (m + n) ⊢ n + (m + 1) = Nat.succ (m + n)
no goals
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Debug/AddComm.lean
add_comm
[1, 1]
[7, 15]
apply congrArg
n m : Nat ⊢ Nat.succ (n + m) = Nat.succ (m + n)
case h n m : Nat ⊢ n + m = m + n
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Debug/AddComm.lean
add_comm
[1, 1]
[7, 15]
apply Nat.add_comm
case h n m : Nat ⊢ n + m = m + n
no goals
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Typechecker/TypecheckInLurk.lean
add_comm
[17, 1]
[23, 15]
have : Nat.succ (n + m) = Nat.succ (m + n) := by apply congrArg; apply Nat.add_comm
n m : Nat ⊢ n + (m + 1) = m + 1 + n
n m : Nat this : Nat.succ (n + m) = Nat.succ (m + n) ⊢ n + (m + 1) = m + 1 + n
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Typechecker/TypecheckInLurk.lean
add_comm
[17, 1]
[23, 15]
rw [Nat.succ_add m n]
n m : Nat this : Nat.succ (n + m) = Nat.succ (m + n) ⊢ n + (m + 1) = m + 1 + n
n m : Nat this : Nat.succ (n + m) = Nat.succ (m + n) ⊢ n + (m + 1) = Nat.succ (m + n)
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Typechecker/TypecheckInLurk.lean
add_comm
[17, 1]
[23, 15]
apply this
n m : Nat this : Nat.succ (n + m) = Nat.succ (m + n) ⊢ n + (m + 1) = Nat.succ (m + n)
no goals
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Typechecker/TypecheckInLurk.lean
add_comm
[17, 1]
[23, 15]
apply congrArg
n m : Nat ⊢ Nat.succ (n + m) = Nat.succ (m + n)
case h n m : Nat ⊢ n + m = m + n
https://github.com/lurk-lab/yatima.git
d9f20f51bca748878b8561661fe8bc19a7dba609
Fixtures/Typechecker/TypecheckInLurk.lean
add_comm
[17, 1]
[23, 15]
apply Nat.add_comm
case h n m : Nat ⊢ n + m = m + n
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
intros p h₃ h₄
α : Type inst : Model α s t : α f : Form h₁ : s ≤ t g : Form h₂ : s⊨~g ⊢ t⊨~g
α : Type inst : Model α s t : α f : Form h₁ : s ≤ t g : Form h₂ : s⊨~g p : Model.primes h₃ : t ≤ ↑p h₄ : ↑(p*)⊨g ⊢ False
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
exact h₂ (le_trans h₁ h₃) h₄
α : Type inst : Model α s t : α f : Form h₁ : s ≤ t g : Form h₂ : s⊨~g p : Model.primes h₃ : t ≤ ↑p h₄ : ↑(p*)⊨g ⊢ False
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
apply And.intro
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f&g ⊢ t⊨f&g
case left α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f&g ⊢ t⊨f case right α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f&g ⊢ t⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
case left => exact upwardsClosure h₁ h₂.left
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f&g ⊢ t⊨f
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
case right => exact upwardsClosure h₁ h₂.right
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f&g ⊢ t⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
exact upwardsClosure h₁ h₂.left
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f&g ⊢ t⊨f
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
exact upwardsClosure h₁ h₂.right
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f&g ⊢ t⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
intros p h₃
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f¦g ⊢ t⊨f¦g
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f¦g p : Model.primes h₃ : t ≤ ↑p ⊢ ↑p⊨f ∨ ↑p⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
apply Or.elim (h₂ (le_trans' h₃ h₁))
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f¦g p : Model.primes h₃ : t ≤ ↑p ⊢ ↑p⊨f ∨ ↑p⊨g
case left α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f¦g p : Model.primes h₃ : t ≤ ↑p ⊢ ↑p⊨f → ↑p⊨f ∨ ↑p⊨g case right α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f¦g p : Model.primes h₃ : t ≤ ↑p ⊢ ↑p⊨g → ↑p⊨f ∨ ↑p⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
case left => intro h₄; exact Or.inl h₄
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f¦g p : Model.primes h₃ : t ≤ ↑p ⊢ ↑p⊨f → ↑p⊨f ∨ ↑p⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
case right => intro h₄; exact Or.inr h₄
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f¦g p : Model.primes h₃ : t ≤ ↑p ⊢ ↑p⊨g → ↑p⊨f ∨ ↑p⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
intro h₄
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f¦g p : Model.primes h₃ : t ≤ ↑p ⊢ ↑p⊨f → ↑p⊨f ∨ ↑p⊨g
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f¦g p : Model.primes h₃ : t ≤ ↑p h₄ : ↑p⊨f ⊢ ↑p⊨f ∨ ↑p⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
exact Or.inl h₄
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f¦g p : Model.primes h₃ : t ≤ ↑p h₄ : ↑p⊨f ⊢ ↑p⊨f ∨ ↑p⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
intro h₄
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f¦g p : Model.primes h₃ : t ≤ ↑p ⊢ ↑p⊨g → ↑p⊨f ∨ ↑p⊨g
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f¦g p : Model.primes h₃ : t ≤ ↑p h₄ : ↑p⊨g ⊢ ↑p⊨f ∨ ↑p⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
exact Or.inr h₄
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f¦g p : Model.primes h₃ : t ≤ ↑p h₄ : ↑p⊨g ⊢ ↑p⊨f ∨ ↑p⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
intros u h₃
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f⊃g ⊢ t⊨f⊃g
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f⊃g u : α h₃ : u⊨f ⊢ t∙u⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
have l₁ : s ∙ u ≤ t ∙ u := inst.appMonotoneRight u h₁
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f⊃g u : α h₃ : u⊨f ⊢ t∙u⊨g
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f⊃g u : α h₃ : u⊨f l₁ : s∙u ≤ t∙u ⊢ t∙u⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
have l₂ : (s ∙ u) ⊨ g := h₂ h₃
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f⊃g u : α h₃ : u⊨f l₁ : s∙u ≤ t∙u ⊢ t∙u⊨g
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f⊃g u : α h₃ : u⊨f l₁ : s∙u ≤ t∙u l₂ : s∙u⊨g ⊢ t∙u⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
upwardsClosure
[23, 1]
[38, 53]
exact upwardsClosure l₁ l₂
α : Type inst : Model α s t : α f✝ : Form h₁ : s ≤ t f g : Form h₂ : s⊨f⊃g u : α h₃ : u⊨f l₁ : s∙u ≤ t∙u l₂ : s∙u⊨g ⊢ t∙u⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
intros p h₂ h₃
α : Type inst : Model α t : α f✝ f : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨~f ⊢ t⊨~f
α : Type inst : Model α t : α f✝ f : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨~f p : Model.primes h₂ : t ≤ ↑p h₃ : ↑(p*)⊨f ⊢ False
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
exact h₁ p h₂ (le_refl p.val) h₃
α : Type inst : Model α t : α f✝ f : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨~f p : Model.primes h₂ : t ≤ ↑p h₃ : ↑(p*)⊨f ⊢ False
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
apply And.intro
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g ⊢ t⊨f&g
case left α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g ⊢ t⊨f case right α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g ⊢ t⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
case left => have l₁ : ∀p : inst.primes, t ≤ p → p ⊨ f := by intros p h₂ exact (h₁ p h₂).left exact primeDetermination l₁
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g ⊢ t⊨f
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
case right => have l₁ : ∀p : inst.primes, t ≤ p → p ⊨ g := by intros p h₂ exact (h₁ p h₂).right exact primeDetermination l₁
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g ⊢ t⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
have l₁ : ∀p : inst.primes, t ≤ p → p ⊨ f := by intros p h₂ exact (h₁ p h₂).left
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g ⊢ t⊨f
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g l₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f ⊢ t⊨f
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
exact primeDetermination l₁
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g l₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f ⊢ t⊨f
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
intros p h₂
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g ⊢ ∀ (p : Model.primes), t ≤ ↑p → p⊨f
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g p : Model.primes h₂ : t ≤ ↑p ⊢ p⊨f
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
exact (h₁ p h₂).left
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g p : Model.primes h₂ : t ≤ ↑p ⊢ p⊨f
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
have l₁ : ∀p : inst.primes, t ≤ p → p ⊨ g := by intros p h₂ exact (h₁ p h₂).right
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g ⊢ t⊨g
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g l₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨g ⊢ t⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
exact primeDetermination l₁
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g l₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨g ⊢ t⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
intros p h₂
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g ⊢ ∀ (p : Model.primes), t ≤ ↑p → p⊨g
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g p : Model.primes h₂ : t ≤ ↑p ⊢ p⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
exact (h₁ p h₂).right
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f&g p : Model.primes h₂ : t ≤ ↑p ⊢ p⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
intros p h₂
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f¦g ⊢ t⊨f¦g
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f¦g p : Model.primes h₂ : t ≤ ↑p ⊢ ↑p⊨f ∨ ↑p⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
cases h₁ p h₂ (le_refl p.val)
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f¦g p : Model.primes h₂ : t ≤ ↑p ⊢ ↑p⊨f ∨ ↑p⊨g
case inl α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f¦g p : Model.primes h₂ : t ≤ ↑p h✝ : ↑p⊨f ⊢ ↑p⊨f ∨ ↑p⊨g case inr α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f¦g p : Model.primes h₂ : t ≤ ↑p h✝ : ↑p⊨g ⊢ ↑p⊨f ∨ ↑p⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
case inl => apply Or.inl; assumption
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f¦g p : Model.primes h₂ : t ≤ ↑p h✝ : ↑p⊨f ⊢ ↑p⊨f ∨ ↑p⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
case inr => apply Or.inr; assumption
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f¦g p : Model.primes h₂ : t ≤ ↑p h✝ : ↑p⊨g ⊢ ↑p⊨f ∨ ↑p⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
apply Or.inl
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f¦g p : Model.primes h₂ : t ≤ ↑p h✝ : ↑p⊨f ⊢ ↑p⊨f ∨ ↑p⊨g
case h α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f¦g p : Model.primes h₂ : t ≤ ↑p h✝ : ↑p⊨f ⊢ ↑p⊨f
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
assumption
case h α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f¦g p : Model.primes h₂ : t ≤ ↑p h✝ : ↑p⊨f ⊢ ↑p⊨f
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
apply Or.inr
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f¦g p : Model.primes h₂ : t ≤ ↑p h✝ : ↑p⊨g ⊢ ↑p⊨f ∨ ↑p⊨g
case h α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f¦g p : Model.primes h₂ : t ≤ ↑p h✝ : ↑p⊨g ⊢ ↑p⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
assumption
case h α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f¦g p : Model.primes h₂ : t ≤ ↑p h✝ : ↑p⊨g ⊢ ↑p⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
intros u h₂
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f⊃g ⊢ t⊨f⊃g
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f⊃g u : α h₂ : u⊨f ⊢ t∙u⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
apply primeDetermination
α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f⊃g u : α h₂ : u⊨f ⊢ t∙u⊨g
case h₁ α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f⊃g u : α h₂ : u⊨f ⊢ ∀ (p : Model.primes), t∙u ≤ ↑p → p⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
intros p h₃
case h₁ α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f⊃g u : α h₂ : u⊨f ⊢ ∀ (p : Model.primes), t∙u ≤ ↑p → p⊨g
case h₁ α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f⊃g u : α h₂ : u⊨f p : Model.primes h₃ : t∙u ≤ ↑p ⊢ p⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
have ⟨q, _, l₃,_,l₄,_⟩ : ∃q r : inst.primes, t ≤ q ∧ u ≤ r ∧ (↑q ∙ u) ≤ p ∧ (t ∙ r) ≤ p.val := inst.appBounding t u p h₃
case h₁ α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f⊃g u : α h₂ : u⊨f p : Model.primes h₃ : t∙u ≤ ↑p ⊢ p⊨g
case h₁ α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f⊃g u : α h₂ : u⊨f p : Model.primes h₃ : t∙u ≤ ↑p q w✝ : Subtype Model.prime l₃ : t ≤ ↑q left✝ : u ≤ ↑w✝ l₄ : ↑q∙u ≤ ↑p right✝ : t∙↑w✝ ≤ ↑p ⊢ p⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
have l₅ : (↑q ∙ u) ⊨ g := h₁ q l₃ h₂
case h₁ α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f⊃g u : α h₂ : u⊨f p : Model.primes h₃ : t∙u ≤ ↑p q w✝ : Subtype Model.prime l₃ : t ≤ ↑q left✝ : u ≤ ↑w✝ l₄ : ↑q∙u ≤ ↑p right✝ : t∙↑w✝ ≤ ↑p ⊢ p⊨g
case h₁ α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f⊃g u : α h₂ : u⊨f p : Model.primes h₃ : t∙u ≤ ↑p q w✝ : Subtype Model.prime l₃ : t ≤ ↑q left✝ : u ≤ ↑w✝ l₄ : ↑q∙u ≤ ↑p right✝ : t∙↑w✝ ≤ ↑p l₅ : ↑q∙u⊨g ⊢ p⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
primeDetermination
[40, 1]
[65, 53]
exact upwardsClosure l₄ l₅
case h₁ α : Type inst : Model α t : α f✝ f g : Form h₁ : ∀ (p : Model.primes), t ≤ ↑p → p⊨f⊃g u : α h₂ : u⊨f p : Model.primes h₃ : t∙u ≤ ↑p q w✝ : Subtype Model.prime l₃ : t ≤ ↑q left✝ : u ≤ ↑w✝ l₄ : ↑q∙u ≤ ↑p right✝ : t∙↑w✝ ≤ ↑p l₅ : ↑q∙u⊨g ⊢ p⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
starCompatRight
[67, 1]
[71, 32]
intro h₁ h₂
α : Type inst : Model α p : Model.primes f : Form ⊢ p*⊨f → ¬p⊨~f
α : Type inst : Model α p : Model.primes f : Form h₁ : p*⊨f h₂ : p⊨~f ⊢ False
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
starCompatRight
[67, 1]
[71, 32]
unfold psatisfies at h₂
α : Type inst : Model α p : Model.primes f : Form h₁ : p*⊨f h₂ : p⊨~f ⊢ False
α : Type inst : Model α p : Model.primes f : Form h₁ : p*⊨f h₂ : ↑p⊨~f ⊢ False
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
starCompatRight
[67, 1]
[71, 32]
unfold satisfies at h₂
α : Type inst : Model α p : Model.primes f : Form h₁ : p*⊨f h₂ : ↑p⊨~f ⊢ False
α : Type inst : Model α p : Model.primes f : Form h₁ : p*⊨f h₂ : ∀ {p_1 : Model.primes}, ↑p ≤ ↑p_1 → ¬↑(p_1*)⊨f ⊢ False
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
starCompatRight
[67, 1]
[71, 32]
exact h₂ (le_refl p.val) h₁
α : Type inst : Model α p : Model.primes f : Form h₁ : p*⊨f h₂ : ∀ {p_1 : Model.primes}, ↑p ≤ ↑p_1 → ¬↑(p_1*)⊨f ⊢ False
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
logicInIdentity
[73, 1]
[82, 18]
apply Iff.intro
α : Type inst : Model α f g : Form ⊢ Model.identity⊨f⊃g ↔ ∀ (x : α), x⊨f → x⊨g
case mp α : Type inst : Model α f g : Form ⊢ Model.identity⊨f⊃g → ∀ (x : α), x⊨f → x⊨g case mpr α : Type inst : Model α f g : Form ⊢ (∀ (x : α), x⊨f → x⊨g) → Model.identity⊨f⊃g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
logicInIdentity
[73, 1]
[82, 18]
case mp => intros h₁ x h₂ rw [←inst.appLeftIdent x] exact h₁ h₂
α : Type inst : Model α f g : Form ⊢ Model.identity⊨f⊃g → ∀ (x : α), x⊨f → x⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
logicInIdentity
[73, 1]
[82, 18]
case mpr => intro h₁ u h₂ rw [inst.appLeftIdent u] exact h₁ u h₂
α : Type inst : Model α f g : Form ⊢ (∀ (x : α), x⊨f → x⊨g) → Model.identity⊨f⊃g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
logicInIdentity
[73, 1]
[82, 18]
intros h₁ x h₂
α : Type inst : Model α f g : Form ⊢ Model.identity⊨f⊃g → ∀ (x : α), x⊨f → x⊨g
α : Type inst : Model α f g : Form h₁ : Model.identity⊨f⊃g x : α h₂ : x⊨f ⊢ x⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
logicInIdentity
[73, 1]
[82, 18]
rw [←inst.appLeftIdent x]
α : Type inst : Model α f g : Form h₁ : Model.identity⊨f⊃g x : α h₂ : x⊨f ⊢ x⊨g
α : Type inst : Model α f g : Form h₁ : Model.identity⊨f⊃g x : α h₂ : x⊨f ⊢ Model.identity∙x⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
logicInIdentity
[73, 1]
[82, 18]
exact h₁ h₂
α : Type inst : Model α f g : Form h₁ : Model.identity⊨f⊃g x : α h₂ : x⊨f ⊢ Model.identity∙x⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
logicInIdentity
[73, 1]
[82, 18]
intro h₁ u h₂
α : Type inst : Model α f g : Form ⊢ (∀ (x : α), x⊨f → x⊨g) → Model.identity⊨f⊃g
α : Type inst : Model α f g : Form h₁ : ∀ (x : α), x⊨f → x⊨g u : α h₂ : u⊨f ⊢ Model.identity∙u⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
logicInIdentity
[73, 1]
[82, 18]
rw [inst.appLeftIdent u]
α : Type inst : Model α f g : Form h₁ : ∀ (x : α), x⊨f → x⊨g u : α h₂ : u⊨f ⊢ Model.identity∙u⊨g
α : Type inst : Model α f g : Form h₁ : ∀ (x : α), x⊨f → x⊨g u : α h₂ : u⊨f ⊢ u⊨g
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
logicInIdentity
[73, 1]
[82, 18]
exact h₁ u h₂
α : Type inst : Model α f g : Form h₁ : ∀ (x : α), x⊨f → x⊨g u : α h₂ : u⊨f ⊢ u⊨g
no goals
https://github.com/gleachkr/Completeness-For-Fine-Semantics.git
0d8cc9a4c9c53181a2bf1541d2ed5a39c2593f0f
Fine/Semantics/Satisfaction.lean
starCompatLeft
[88, 1]
[94, 29]
intros h₁
α : Type inst : Model α p : Model.primes f : Form ⊢ ¬p⊨~f → p*⊨f
α : Type inst : Model α p : Model.primes f : Form h₁ : ¬p⊨~f ⊢ p*⊨f