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/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | apply Iff.intro | case h
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
β’ y β image f (W β© X) β y β image f W β© image f X | case h.mp
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
β’ y β image f (W β© X) β y β image f W β© image f X
case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
β’ y β image f W β© image f X β y β image f (W β© X) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
β’ y β image f (W β© X) β y β image f W β© image f X
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | assume h2 : y β image f (W β© X) | case h.mp
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
β’ y β image f (W β© X) β y β image f W β© image f X | case h.mp
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : y β image f (W β© X)
β’ y β image f W β© image f X | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
β’ y β image f (W β© X) β y β image f W β© image f X
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | show y β image f W β© image f X from Theorem_5_5_2_1 f W X h2 | case h.mp
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : y β image f (W β© X)
β’ y β image f W β© image f X | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mp
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : y β image f (W β© X)
β’ y β image f W β© image f X
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | assume h2 : y β image f W β© image f X | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
β’ y β image f W β© image f X β y β image f (W β© X) | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : y β image f W β© image f X
β’ y β image f (W β© X) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
β’ y β image f W β© image f X β y β image f (W β© X)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | define at h2 | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : y β image f W β© image f X
β’ y β image f (W β© X) | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : y β image f W β§ y β image f X
β’ y β image f (W β© X) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : y β image f W β© image f X
β’ y β image f (W β© X)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | rewrite [image_def, image_def] at h2 | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : y β image f W β§ y β image f X
β’ y β image f (W β© X) | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
β’ y β image f (W β© X) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : y β image f W β§ y β image f X
β’ y β image f (W β© X)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | obtain (x1 : A) (h3 : x1 β W β§ f x1 = y) from h2.left | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
β’ y β image f (W β© X) | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
β’ y β image f (W β© X) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
β’ y β image f (W β© X)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | obtain (x2 : A) (h4 : x2 β X β§ f x2 = y) from h2.right | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
β’ y β image f (W β© X) | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
β’ y β image f (W β© X) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
β’ y β image f (W β© X)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | have h5 : f x2 = y := h4.right | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
β’ y β image f (W β© X) | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
h5 : f x2 = y
β’ y β image f (W β© X) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
β’ y β image f (W β© X)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | rewrite [βh3.right] at h5 | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
h5 : f x2 = y
β’ y β image f (W β© X) | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
h5 : f x2 = f x1
β’ y β image f (W β© X) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
h5 : f x2 = y
β’ y β image f (W β© X)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | define at h1 | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
h5 : f x2 = f x1
β’ y β image f (W β© X) | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : β (x1 x2 : A), f x1 = f x2 β x1 = x2
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
h5 : f x2 = f x1
β’ y β image f (W β© X) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : one_to_one f
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
h5 : f x2 = f x1
β’ y β image f (W β© X)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | have h6 : x2 = x1 := h1 x2 x1 h5 | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : β (x1 x2 : A), f x1 = f x2 β x1 = x2
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
h5 : f x2 = f x1
β’ y β image f (W β© X) | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : β (x1 x2 : A), f x1 = f x2 β x1 = x2
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
h5 : f x2 = f x1
h6 : x2 = x1
β’ y β image f (W β© X) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : β (x1 x2 : A), f x1 = f x2 β x1 = x2
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
h5 : f x2 = f x1
β’ y β image f (W β© X)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | rewrite [h6] at h4 | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : β (x1 x2 : A), f x1 = f x2 β x1 = x2
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
h5 : f x2 = f x1
h6 : x2 = x1
β’ y β image f (W β© X) | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : β (x1 x2 : A), f x1 = f x2 β x1 = x2
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x1 β X β§ f x1 = y
h5 : f x2 = f x1
h6 : x2 = x1
β’ y β image f (W β© X) | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : β (x1 x2 : A), f x1 = f x2 β x1 = x2
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x2 β X β§ f x2 = y
h5 : f x2 = f x1
h6 : x2 = x1
β’ y β image f (W β© X)
TACTIC:
|
https://github.com/djvelleman/HTPILeanPackage.git | 4d23e94fff351c65b5e1345c43451f2aa9908c27 | HTPILib/Chap5.lean | HTPI.Theorem_5_5_2_2 | [356, 1] | [380, 7] | show y β image f (W β© X) from
Exists.intro x1 (And.intro (And.intro h3.left h4.left) h3.right) | case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : β (x1 x2 : A), f x1 = f x2 β x1 = x2
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x1 β X β§ f x1 = y
h5 : f x2 = f x1
h6 : x2 = x1
β’ y β image f (W β© X) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
A B : Type
f : A β B
W X : Set A
h1 : β (x1 x2 : A), f x1 = f x2 β x1 = x2
y : B
h2 : (β x β W, f x = y) β§ β x β X, f x = y
x1 : A
h3 : x1 β W β§ f x1 = y
x2 : A
h4 : x1 β X β§ f x1 = y
h5 : f x2 = f x1
h6 : x2 = x1
β’ y β image f (W β© X)
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_trans | [70, 1] | [75, 27] | intro hyp1 hyp2 k w b dHyp | n : β
cl1 cl2 cl3 : Clause n
β’ cl1βcl2 β cl2βcl3 β cl1βcl3 | n : β
cl1 cl2 cl3 : Clause n
hyp1 : cl1βcl2
hyp2 : cl2βcl3
k : β
w : k < n
b : Bool
dHyp : get' cl3 k w = some b
β’ get' cl1 k w = some b | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 cl3 : Clause n
β’ cl1βcl2 β cl2βcl3 β cl1βcl3
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_trans | [70, 1] | [75, 27] | apply hyp1 | n : β
cl1 cl2 cl3 : Clause n
hyp1 : cl1βcl2
hyp2 : cl2βcl3
k : β
w : k < n
b : Bool
dHyp : get' cl3 k w = some b
β’ get' cl1 k w = some b | case a
n : β
cl1 cl2 cl3 : Clause n
hyp1 : cl1βcl2
hyp2 : cl2βcl3
k : β
w : k < n
b : Bool
dHyp : get' cl3 k w = some b
β’ get' cl2 k w = some b | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 cl3 : Clause n
hyp1 : cl1βcl2
hyp2 : cl2βcl3
k : β
w : k < n
b : Bool
dHyp : get' cl3 k w = some b
β’ get' cl1 k w = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_trans | [70, 1] | [75, 27] | apply hyp2 | case a
n : β
cl1 cl2 cl3 : Clause n
hyp1 : cl1βcl2
hyp2 : cl2βcl3
k : β
w : k < n
b : Bool
dHyp : get' cl3 k w = some b
β’ get' cl2 k w = some b | case a.a
n : β
cl1 cl2 cl3 : Clause n
hyp1 : cl1βcl2
hyp2 : cl2βcl3
k : β
w : k < n
b : Bool
dHyp : get' cl3 k w = some b
β’ get' cl3 k w = some b | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n : β
cl1 cl2 cl3 : Clause n
hyp1 : cl1βcl2
hyp2 : cl2βcl3
k : β
w : k < n
b : Bool
dHyp : get' cl3 k w = some b
β’ get' cl2 k w = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_trans | [70, 1] | [75, 27] | apply dHyp | case a.a
n : β
cl1 cl2 cl3 : Clause n
hyp1 : cl1βcl2
hyp2 : cl2βcl3
k : β
w : k < n
b : Bool
dHyp : get' cl3 k w = some b
β’ get' cl3 k w = some b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
n : β
cl1 cl2 cl3 : Clause n
hyp1 : cl1βcl2
hyp2 : cl2βcl3
k : β
w : k < n
b : Bool
dHyp : get' cl3 k w = some b
β’ get' cl3 k w = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_prepend | [77, 1] | [90, 34] | intro hyp1 hyp2 k | n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
β’ v1 β₯ v2 β cl1βcl2 β v1 ::α΅₯ cl1βv2 ::α΅₯ cl2 | n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k : β
β’ β (kw : k < succ n) (b : Bool), get' (v2 ::α΅₯ cl2) k kw = some b β get' (v1 ::α΅₯ cl1) k kw = some b | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
β’ v1 β₯ v2 β cl1βcl2 β v1 ::α΅₯ cl1βv2 ::α΅₯ cl2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_prepend | [77, 1] | [90, 34] | match k with
| zero =>
intro w b hb
exact hyp1 b hb
| j + 1 =>
intro kw b hb
have w : j < n := by
apply le_of_succ_le_succ
exact kw
exact hyp2 j w b hb | n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k : β
β’ β (kw : k < succ n) (b : Bool), get' (v2 ::α΅₯ cl2) k kw = some b β get' (v1 ::α΅₯ cl1) k kw = some b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k : β
β’ β (kw : k < succ n) (b : Bool), get' (v2 ::α΅₯ cl2) k kw = some b β get' (v1 ::α΅₯ cl1) k kw = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_prepend | [77, 1] | [90, 34] | intro w b hb | n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k : β
β’ β (kw : zero < succ n) (b : Bool), get' (v2 ::α΅₯ cl2) zero kw = some b β get' (v1 ::α΅₯ cl1) zero kw = some b | n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k : β
w : zero < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) zero w = some b
β’ get' (v1 ::α΅₯ cl1) zero w = some b | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k : β
β’ β (kw : zero < succ n) (b : Bool), get' (v2 ::α΅₯ cl2) zero kw = some b β get' (v1 ::α΅₯ cl1) zero kw = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_prepend | [77, 1] | [90, 34] | exact hyp1 b hb | n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k : β
w : zero < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) zero w = some b
β’ get' (v1 ::α΅₯ cl1) zero w = some b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k : β
w : zero < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) zero w = some b
β’ get' (v1 ::α΅₯ cl1) zero w = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_prepend | [77, 1] | [90, 34] | intro kw b hb | n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k j : β
β’ β (kw : j + 1 < succ n) (b : Bool), get' (v2 ::α΅₯ cl2) (j + 1) kw = some b β get' (v1 ::α΅₯ cl1) (j + 1) kw = some b | n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k j : β
kw : j + 1 < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) (j + 1) kw = some b
β’ get' (v1 ::α΅₯ cl1) (j + 1) kw = some b | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k j : β
β’ β (kw : j + 1 < succ n) (b : Bool), get' (v2 ::α΅₯ cl2) (j + 1) kw = some b β get' (v1 ::α΅₯ cl1) (j + 1) kw = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_prepend | [77, 1] | [90, 34] | have w : j < n := by
apply le_of_succ_le_succ
exact kw | n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k j : β
kw : j + 1 < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) (j + 1) kw = some b
β’ get' (v1 ::α΅₯ cl1) (j + 1) kw = some b | n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k j : β
kw : j + 1 < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) (j + 1) kw = some b
w : j < n
β’ get' (v1 ::α΅₯ cl1) (j + 1) kw = some b | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k j : β
kw : j + 1 < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) (j + 1) kw = some b
β’ get' (v1 ::α΅₯ cl1) (j + 1) kw = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_prepend | [77, 1] | [90, 34] | exact hyp2 j w b hb | n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k j : β
kw : j + 1 < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) (j + 1) kw = some b
w : j < n
β’ get' (v1 ::α΅₯ cl1) (j + 1) kw = some b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k j : β
kw : j + 1 < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) (j + 1) kw = some b
w : j < n
β’ get' (v1 ::α΅₯ cl1) (j + 1) kw = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_prepend | [77, 1] | [90, 34] | apply le_of_succ_le_succ | n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k j : β
kw : j + 1 < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) (j + 1) kw = some b
β’ j < n | case a
n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k j : β
kw : j + 1 < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) (j + 1) kw = some b
β’ succ (succ j) β€ succ n | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k j : β
kw : j + 1 < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) (j + 1) kw = some b
β’ j < n
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_prepend | [77, 1] | [90, 34] | exact kw | case a
n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k j : β
kw : j + 1 < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) (j + 1) kw = some b
β’ succ (succ j) β€ succ n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
n : β
v1 v2 : Option Bool
cl1 cl2 : Clause n
hyp1 : v1 β₯ v2
hyp2 : cl1βcl2
k j : β
kw : j + 1 < succ n
b : Bool
hb : get' (v2 ::α΅₯ cl2) (j + 1) kw = some b
β’ succ (succ j) β€ succ n
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_implies_clauseContains_beyond | [98, 1] | [101, 19] | intro h k kw _ b | n : β
cl1 cl2 : Clause n
m : β
β’ cl1βcl2 β clauseContainsTail cl1 cl2 m | n : β
cl1 cl2 : Clause n
m : β
h : cl1βcl2
k : β
kw : k < n
aβ : m β€ k
b : Bool
β’ get' cl2 k kw = some b β get' cl1 k kw = some b | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 : Clause n
m : β
β’ cl1βcl2 β clauseContainsTail cl1 cl2 m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_implies_clauseContains_beyond | [98, 1] | [101, 19] | exact h k kw b | n : β
cl1 cl2 : Clause n
m : β
h : cl1βcl2
k : β
kw : k < n
aβ : m β€ k
b : Bool
β’ get' cl2 k kw = some b β get' cl1 k kw = some b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 : Clause n
m : β
h : cl1βcl2
k : β
kw : k < n
aβ : m β€ k
b : Bool
β’ get' cl2 k kw = some b β get' cl1 k kw = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_beyond_zero_implies_contains | [103, 1] | [106, 35] | intro h k kw b | n : β
cl1 cl2 : Clause n
β’ clauseContainsTail cl1 cl2 zero β cl1βcl2 | n : β
cl1 cl2 : Clause n
h : clauseContainsTail cl1 cl2 zero
k : β
kw : k < n
b : Bool
β’ get' cl2 k kw = some b β get' cl1 k kw = some b | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 : Clause n
β’ clauseContainsTail cl1 cl2 zero β cl1βcl2
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_beyond_zero_implies_contains | [103, 1] | [106, 35] | exact h k kw (Nat.zero_le _) b | n : β
cl1 cl2 : Clause n
h : clauseContainsTail cl1 cl2 zero
k : β
kw : k < n
b : Bool
β’ get' cl2 k kw = some b β get' cl1 k kw = some b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 : Clause n
h : clauseContainsTail cl1 cl2 zero
k : β
kw : k < n
b : Bool
β’ get' cl2 k kw = some b β get' cl1 k kw = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | sat_of_contained_sat | [111, 1] | [117, 24] | intro num_clauses valuation | n : β
cl1 cl2 : Clause n
β’ cl1βcl2 β β (valuation : Valuation n), ClauseSat cl2 valuation β ClauseSat cl1 valuation | n : β
cl1 cl2 : Clause n
num_clauses : cl1βcl2
valuation : Valuation n
β’ ClauseSat cl2 valuation β ClauseSat cl1 valuation | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 : Clause n
β’ cl1βcl2 β β (valuation : Valuation n), ClauseSat cl2 valuation β ClauseSat cl1 valuation
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | sat_of_contained_sat | [111, 1] | [117, 24] | intro β¨j, jw, vsβ© | n : β
cl1 cl2 : Clause n
num_clauses : cl1βcl2
valuation : Valuation n
β’ ClauseSat cl2 valuation β ClauseSat cl1 valuation | n : β
cl1 cl2 : Clause n
num_clauses : cl1βcl2
valuation : Valuation n
j : β
jw : j < n
vs : VarSat (Vector.get cl2 { val := j, isLt := jw }) (Vector.get valuation { val := j, isLt := jw })
β’ ClauseSat cl1 valuation | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 : Clause n
num_clauses : cl1βcl2
valuation : Valuation n
β’ ClauseSat cl2 valuation β ClauseSat cl1 valuation
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | sat_of_contained_sat | [111, 1] | [117, 24] | let lem0 : cl2.get' j jw = some (valuation.get' j jw) := vs | n : β
cl1 cl2 : Clause n
num_clauses : cl1βcl2
valuation : Valuation n
j : β
jw : j < n
vs : VarSat (Vector.get cl2 { val := j, isLt := jw }) (Vector.get valuation { val := j, isLt := jw })
β’ ClauseSat cl1 valuation | n : β
cl1 cl2 : Clause n
num_clauses : cl1βcl2
valuation : Valuation n
j : β
jw : j < n
vs : VarSat (Vector.get cl2 { val := j, isLt := jw }) (Vector.get valuation { val := j, isLt := jw })
lem0 : get' cl2 j jw = some (get' valuation j jw) := vs
β’ ClauseSat cl1 valuation | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 : Clause n
num_clauses : cl1βcl2
valuation : Valuation n
j : β
jw : j < n
vs : VarSat (Vector.get cl2 { val := j, isLt := jw }) (Vector.get valuation { val := j, isLt := jw })
β’ ClauseSat cl1 valuation
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | sat_of_contained_sat | [111, 1] | [117, 24] | let lem1 : get' cl1 j jw = some (get' valuation j jw) := num_clauses j jw (valuation.get' j jw) lem0 | n : β
cl1 cl2 : Clause n
num_clauses : cl1βcl2
valuation : Valuation n
j : β
jw : j < n
vs : VarSat (Vector.get cl2 { val := j, isLt := jw }) (Vector.get valuation { val := j, isLt := jw })
lem0 : get' cl2 j jw = some (get' valuation j jw) := vs
β’ ClauseSat cl1 valuation | n : β
cl1 cl2 : Clause n
num_clauses : cl1βcl2
valuation : Valuation n
j : β
jw : j < n
vs : VarSat (Vector.get cl2 { val := j, isLt := jw }) (Vector.get valuation { val := j, isLt := jw })
lem0 : get' cl2 j jw = some (get' valuation j jw) := vs
lem1 : get' cl1 j jw = some (get' valuation j jw) := num_clauses j jw (get... | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 : Clause n
num_clauses : cl1βcl2
valuation : Valuation n
j : β
jw : j < n
vs : VarSat (Vector.get cl2 { val := j, isLt := jw }) (Vector.get valuation { val := j, isLt := jw })
lem0 : get' cl2 j jw = some (get' valuation j jw) := vs
β’ ClauseSat c... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | sat_of_contained_sat | [111, 1] | [117, 24] | exact β¨j, jw, lem1β© | n : β
cl1 cl2 : Clause n
num_clauses : cl1βcl2
valuation : Valuation n
j : β
jw : j < n
vs : VarSat (Vector.get cl2 { val := j, isLt := jw }) (Vector.get valuation { val := j, isLt := jw })
lem0 : get' cl2 j jw = some (get' valuation j jw) := vs
lem1 : get' cl1 j jw = some (get' valuation j jw) := num_clauses j jw (get... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 : Clause n
num_clauses : cl1βcl2
valuation : Valuation n
j : β
jw : j < n
vs : VarSat (Vector.get cl2 { val := j, isLt := jw }) (Vector.get valuation { val := j, isLt := jw })
lem0 : get' cl2 j jw = some (get' valuation j jw) := vs
lem1 : get' c... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_beyond_vacuously | [120, 1] | [125, 48] | intro h k kw ineq | n : β
cl1 cl2 : Clause n
m : β
β’ n β€ m β clauseContainsTail cl1 cl2 m | n : β
cl1 cl2 : Clause n
m : β
h : n β€ m
k : β
kw : k < n
ineq : m β€ k
β’ β (b : Bool), get' cl2 k kw = some b β get' cl1 k kw = some b | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 : Clause n
m : β
β’ n β€ m β clauseContainsTail cl1 cl2 m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_beyond_vacuously | [120, 1] | [125, 48] | let inq := Nat.le_trans h ineq | n : β
cl1 cl2 : Clause n
m : β
h : n β€ m
k : β
kw : k < n
ineq : m β€ k
β’ β (b : Bool), get' cl2 k kw = some b β get' cl1 k kw = some b | n : β
cl1 cl2 : Clause n
m : β
h : n β€ m
k : β
kw : k < n
ineq : m β€ k
inq : n β€ k := Nat.le_trans h ineq
β’ β (b : Bool), get' cl2 k kw = some b β get' cl1 k kw = some b | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 : Clause n
m : β
h : n β€ m
k : β
kw : k < n
ineq : m β€ k
β’ β (b : Bool), get' cl2 k kw = some b β get' cl1 k kw = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_beyond_vacuously | [120, 1] | [125, 48] | let inq2 := Nat.lt_of_lt_of_le kw inq | n : β
cl1 cl2 : Clause n
m : β
h : n β€ m
k : β
kw : k < n
ineq : m β€ k
inq : n β€ k := Nat.le_trans h ineq
β’ β (b : Bool), get' cl2 k kw = some b β get' cl1 k kw = some b | n : β
cl1 cl2 : Clause n
m : β
h : n β€ m
k : β
kw : k < n
ineq : m β€ k
inq : n β€ k := Nat.le_trans h ineq
inq2 : k < k := Nat.lt_of_lt_of_le kw inq
β’ β (b : Bool), get' cl2 k kw = some b β get' cl1 k kw = some b | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 : Clause n
m : β
h : n β€ m
k : β
kw : k < n
ineq : m β€ k
inq : n β€ k := Nat.le_trans h ineq
β’ β (b : Bool), get' cl2 k kw = some b β get' cl1 k kw = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Containment.lean | clauseContains_beyond_vacuously | [120, 1] | [125, 48] | exact (False.elim (Nat.lt_irrefl k inq2)) | n : β
cl1 cl2 : Clause n
m : β
h : n β€ m
k : β
kw : k < n
ineq : m β€ k
inq : n β€ k := Nat.le_trans h ineq
inq2 : k < k := Nat.lt_of_lt_of_le kw inq
β’ β (b : Bool), get' cl2 k kw = some b β get' cl1 k kw = some b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
cl1 cl2 : Clause n
m : β
h : n β€ m
k : β
kw : k < n
ineq : m β€ k
inq : n β€ k := Nat.le_trans h ineq
inq2 : k < k := Nat.lt_of_lt_of_le kw inq
β’ β (b : Bool), get' cl2 k kw = some b β get' cl1 k kw = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | get'_contradiction | [33, 1] | [34, 44] | rw [contradiction, Vector.get'_of_Fn'] | n k : β
w : k < n
β’ get' (contradiction n) k w = none | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n k : β
w : k < n
β’ get' (contradiction n) k w = none
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | get_contradiction | [36, 1] | [37, 55] | rw [contradiction, Vector.ofFn', Vector.get_ofFn] | n : β
kw : Fin n
β’ Vector.get (contradiction n) kw = none | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
kw : Fin n
β’ Vector.get (contradiction n) kw = none
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_is_false | [39, 1] | [42, 42] | intro valuation β¨k, β¨b, pβ©β© | n : β
β’ β (valuation : Valuation n), Β¬ClauseSat (contradiction n) valuation | n : β
valuation : Valuation n
k : β
b : k < n
p : VarSat (Vector.get (contradiction n) { val := k, isLt := b }) (Vector.get valuation { val := k, isLt := b })
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
β’ β (valuation : Valuation n), Β¬ClauseSat (contradiction n) valuation
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_is_false | [39, 1] | [42, 42] | simp [get_contradiction, VarSat] at p | n : β
valuation : Valuation n
k : β
b : k < n
p : VarSat (Vector.get (contradiction n) { val := k, isLt := b }) (Vector.get valuation { val := k, isLt := b })
β’ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
valuation : Valuation n
k : β
b : k < n
p : VarSat (Vector.get (contradiction n) { val := k, isLt := b }) (Vector.get valuation { val := k, isLt := b })
β’ False
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_insert_none | [45, 1] | [66, 38] | apply funext | n focus : β
focusLt : focus < n + 1
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) = get' (contradiction (n + 1)) | case h
n focus : β
focusLt : focus < n + 1
β’ β (x : β), FinSeq.insert none n focus focusLt (get' (contradiction n)) x = get' (contradiction (n + 1)) x | Please generate a tactic in lean4 to solve the state.
STATE:
n focus : β
focusLt : focus < n + 1
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) = get' (contradiction (n + 1))
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_insert_none | [45, 1] | [66, 38] | intro j | case h
n focus : β
focusLt : focus < n + 1
β’ β (x : β), FinSeq.insert none n focus focusLt (get' (contradiction n)) x = get' (contradiction (n + 1)) x | case h
n focus : β
focusLt : focus < n + 1
j : β
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j = get' (contradiction (n + 1)) j | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n focus : β
focusLt : focus < n + 1
β’ β (x : β), FinSeq.insert none n focus focusLt (get' (contradiction n)) x = get' (contradiction (n + 1)) x
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_insert_none | [45, 1] | [66, 38] | apply funext | case h
n focus : β
focusLt : focus < n + 1
j : β
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j = get' (contradiction (n + 1)) j | case h.h
n focus : β
focusLt : focus < n + 1
j : β
β’ β (x : j < succ n), FinSeq.insert none n focus focusLt (get' (contradiction n)) j x = get' (contradiction (n + 1)) j x | Please generate a tactic in lean4 to solve the state.
STATE:
case h
n focus : β
focusLt : focus < n + 1
j : β
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j = get' (contradiction (n + 1)) j
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_insert_none | [45, 1] | [66, 38] | intro jw | case h.h
n focus : β
focusLt : focus < n + 1
j : β
β’ β (x : j < succ n), FinSeq.insert none n focus focusLt (get' (contradiction n)) j x = get' (contradiction (n + 1)) j x | case h.h
n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = get' (contradiction (n + 1)) j jw | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
n focus : β
focusLt : focus < n + 1
j : β
β’ β (x : j < succ n), FinSeq.insert none n focus focusLt (get' (contradiction n)) j x = get' (contradiction (n + 1)) j x
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_insert_none | [45, 1] | [66, 38] | rw [get'_contradiction] | case h.h
n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = get' (contradiction (n + 1)) j jw | case h.h
n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = none | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = get' (contradiction (n + 1)) j jw
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_insert_none | [45, 1] | [66, 38] | exact if c : j = focus then
match focus, c, focusLt with
| .(j), rfl, .(jw) =>
by
rw [insert_at_focus]
else by
let i := skipInverse focus j c
let eqn : skip focus i = j := skipInverse_eq focus j c
let iw := skip_preimage_lt focusLt jw eqn
match j, eqn, jw with
| .(skip focus i), rfl, .(skip_le_s... | case h.h
n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = none | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = none
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_insert_none | [45, 1] | [66, 38] | rw [insert_at_focus] | n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : j = focus
β’ FinSeq.insert none n j jw (get' (contradiction n)) j jw = none | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : j = focus
β’ FinSeq.insert none n j jw (get' (contradiction n)) j jw = none
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_insert_none | [45, 1] | [66, 38] | let i := skipInverse focus j c | n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : Β¬j = focus
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = none | n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : Β¬j = focus
i : β := skipInverse focus j c
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = none | Please generate a tactic in lean4 to solve the state.
STATE:
n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : Β¬j = focus
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = none
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_insert_none | [45, 1] | [66, 38] | let eqn : skip focus i = j := skipInverse_eq focus j c | n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : Β¬j = focus
i : β := skipInverse focus j c
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = none | n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : Β¬j = focus
i : β := skipInverse focus j c
eqn : skip focus i = j := skipInverse_eq focus j c
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = none | Please generate a tactic in lean4 to solve the state.
STATE:
n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : Β¬j = focus
i : β := skipInverse focus j c
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = none
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_insert_none | [45, 1] | [66, 38] | let iw := skip_preimage_lt focusLt jw eqn | n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : Β¬j = focus
i : β := skipInverse focus j c
eqn : skip focus i = j := skipInverse_eq focus j c
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = none | n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : Β¬j = focus
i : β := skipInverse focus j c
eqn : skip focus i = j := skipInverse_eq focus j c
iw : i < n := skip_preimage_lt focusLt jw eqn
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = none | Please generate a tactic in lean4 to solve the state.
STATE:
n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : Β¬j = focus
i : β := skipInverse focus j c
eqn : skip focus i = j := skipInverse_eq focus j c
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = none
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_insert_none | [45, 1] | [66, 38] | match j, eqn, jw with
| .(skip focus i), rfl, .(skip_le_succ iw) =>
rw [insert_at_image
none n focus focusLt ((contradiction n).get')
i iw, get'_contradiction] | n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : Β¬j = focus
i : β := skipInverse focus j c
eqn : skip focus i = j := skipInverse_eq focus j c
iw : i < n := skip_preimage_lt focusLt jw eqn
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) j jw = none | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : Β¬j = focus
i : β := skipInverse focus j c
eqn : skip focus i = j := skipInverse_eq focus j c
iw : i < n := skip_preimage_lt focusLt jw eqn
β’ FinSeq.insert none n focus focusLt (get' (contradiction ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | contradiction_insert_none | [45, 1] | [66, 38] | rw [insert_at_image
none n focus focusLt ((contradiction n).get')
i iw, get'_contradiction] | n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : Β¬j = focus
i : β := skipInverse focus j c
eqn : skip focus i = j := skipInverse_eq focus j c
iw : i < n := skip_preimage_lt focusLt jw eqn
β’ FinSeq.insert none n focus focusLt (get' (contradiction n)) (skip focus i) (_ : skip focus i < n + 1) = none | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n focus : β
focusLt : focus < n + 1
j : β
jw : j < succ n
c : Β¬j = focus
i : β := skipInverse focus j c
eqn : skip focus i = j := skipInverse_eq focus j c
iw : i < n := skip_preimage_lt focusLt jw eqn
β’ FinSeq.insert none n focus focusLt (get' (contradiction ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | unitClause_at_literal | [80, 1] | [83, 34] | rw [unitClause, Vector.of_Fn'_get'] | n : β
b : Bool
k : β
w : k < n + 1
β’ get' (unitClause n b k w) k w = some b | n : β
b : Bool
k : β
w : k < n + 1
β’ FinSeq.insert (some b) n k w (get' (contradiction n)) k w = some b | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
b : Bool
k : β
w : k < n + 1
β’ get' (unitClause n b k w) k w = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | unitClause_at_literal | [80, 1] | [83, 34] | apply insert_at_focus | n : β
b : Bool
k : β
w : k < n + 1
β’ FinSeq.insert (some b) n k w (get' (contradiction n)) k w = some b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
b : Bool
k : β
w : k < n + 1
β’ FinSeq.insert (some b) n k w (get' (contradiction n)) k w = some b
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | unitClause_skipping_literal | [85, 1] | [91, 47] | intro i iw | n : β
b : Bool
k : β
w : k < n + 1
β’ β (i : β) (iw : i < n), get' (unitClause n b k w) (skip k i) (_ : skip k i < n + 1) = none | n : β
b : Bool
k : β
w : k < n + 1
i : β
iw : i < n
β’ get' (unitClause n b k w) (skip k i) (_ : skip k i < n + 1) = none | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
b : Bool
k : β
w : k < n + 1
β’ β (i : β) (iw : i < n), get' (unitClause n b k w) (skip k i) (_ : skip k i < n + 1) = none
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | unitClause_skipping_literal | [85, 1] | [91, 47] | rw [unitClause, Vector.of_Fn'_get'] | n : β
b : Bool
k : β
w : k < n + 1
i : β
iw : i < n
β’ get' (unitClause n b k w) (skip k i) (_ : skip k i < n + 1) = none | n : β
b : Bool
k : β
w : k < n + 1
i : β
iw : i < n
β’ FinSeq.insert (some b) n k w (get' (contradiction n)) (skip k i) (_ : skip k i < n + 1) = none | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
b : Bool
k : β
w : k < n + 1
i : β
iw : i < n
β’ get' (unitClause n b k w) (skip k i) (_ : skip k i < n + 1) = none
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | unitClause_skipping_literal | [85, 1] | [91, 47] | let ins := insert_at_image (some b) n k w ((contradiction n).get') i iw | n : β
b : Bool
k : β
w : k < n + 1
i : β
iw : i < n
β’ FinSeq.insert (some b) n k w (get' (contradiction n)) (skip k i) (_ : skip k i < n + 1) = none | n : β
b : Bool
k : β
w : k < n + 1
i : β
iw : i < n
ins : FinSeq.insert (some b) n k w (get' (contradiction n)) (skip k i) (_ : skip k i < n + 1) =
get' (contradiction n) i iw :=
insert_at_image (some b) n k w (get' (contradiction n)) i iw
β’ FinSeq.insert (some b) n k w (get' (contradiction n)) (skip k i) (_ : skip... | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
b : Bool
k : β
w : k < n + 1
i : β
iw : i < n
β’ FinSeq.insert (some b) n k w (get' (contradiction n)) (skip k i) (_ : skip k i < n + 1) = none
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | unitClause_skipping_literal | [85, 1] | [91, 47] | rw [ins, get'_contradiction] | n : β
b : Bool
k : β
w : k < n + 1
i : β
iw : i < n
ins : FinSeq.insert (some b) n k w (get' (contradiction n)) (skip k i) (_ : skip k i < n + 1) =
get' (contradiction n) i iw :=
insert_at_image (some b) n k w (get' (contradiction n)) i iw
β’ FinSeq.insert (some b) n k w (get' (contradiction n)) (skip k i) (_ : skip... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
b : Bool
k : β
w : k < n + 1
i : β
iw : i < n
ins : FinSeq.insert (some b) n k w (get' (contradiction n)) (skip k i) (_ : skip k i < n + 1) =
get' (contradiction n) i iw :=
insert_at_image (some b) n k w (get' (contradiction n)) i iw
β’ FinSeq.insert... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | isPure_of_PureTail_at_zero | [178, 1] | [186, 25] | intro hyp | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
β’ HasPureTail clauses index bound parity zero β IsPure clauses index bound parity | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
hyp : HasPureTail clauses index bound parity zero
β’ IsPure clauses index bound parity | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
β’ HasPureTail clauses index bound parity zero β IsPure clauses index bound parity
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | isPure_of_PureTail_at_zero | [178, 1] | [186, 25] | intro k | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
hyp : HasPureTail clauses index bound parity zero
β’ IsPure clauses index bound parity | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
hyp : HasPureTail clauses index bound parity zero
k : β
β’ β (lt : k < num_clauses),
get' (get' clauses k lt) index bound = none β¨ get' (get' clauses k lt) index bound = some parity | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
hyp : HasPureTail clauses index bound parity zero
β’ IsPure clauses index bound parity
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | isPure_of_PureTail_at_zero | [178, 1] | [186, 25] | intro kw | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
hyp : HasPureTail clauses index bound parity zero
k : β
β’ β (lt : k < num_clauses),
get' (get' clauses k lt) index bound = none β¨ get' (get' clauses k lt) index bound = some parity | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
hyp : HasPureTail clauses index bound parity zero
k : β
kw : k < num_clauses
β’ get' (get' clauses k kw) index bound = none β¨ get' (get' clauses k kw) index bound = some parity | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
hyp : HasPureTail clauses index bound parity zero
k : β
β’ β (lt : k < num_clauses),
get' (get' clauses k lt) index bound = none β¨ get' (get' clauses k lt) ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | isPure_of_PureTail_at_zero | [178, 1] | [186, 25] | exact hyp k kw (Nat.zero_le k) | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
hyp : HasPureTail clauses index bound parity zero
k : β
kw : k < num_clauses
β’ get' (get' clauses k kw) index bound = none β¨ get' (get' clauses k kw) index bound = some parity | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
hyp : HasPureTail clauses index bound parity zero
k : β
kw : k < num_clauses
β’ get' (get' clauses k kw) index bound = none β¨ get' (get' clauses k kw) index bou... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | pureTail_at_end | [188, 1] | [197, 23] | intro k | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
β’ HasPureTail clauses index bound parity m | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
β’ β (lt : k < num_clauses),
m β€ k β get' (get' clauses k lt) index bound = none β¨ get' (get' clauses k lt) index bound = some parity | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
β’ HasPureTail clauses index bound parity m
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | pureTail_at_end | [188, 1] | [197, 23] | intro kw | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
β’ β (lt : k < num_clauses),
m β€ k β get' (get' clauses k lt) index bound = none β¨ get' (get' clauses k lt) index bound = some parity | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
kw : k < num_clauses
β’ m β€ k β get' (get' clauses k kw) index bound = none β¨ get' (get' clauses k kw) index bound = some parity | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
β’ β (lt : k < num_clauses),
m β€ k β get' (get' clauses k lt) index bound = none β¨ get' (get' clauses k lt) index bound = s... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | pureTail_at_end | [188, 1] | [197, 23] | intro ineq | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
kw : k < num_clauses
β’ m β€ k β get' (get' clauses k kw) index bound = none β¨ get' (get' clauses k kw) index bound = some parity | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
kw : k < num_clauses
ineq : m β€ k
β’ get' (get' clauses k kw) index bound = none β¨ get' (get' clauses k kw) index bound = some parity | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
kw : k < num_clauses
β’ m β€ k β get' (get' clauses k kw) index bound = none β¨ get' (get' clauses k kw) index bound = some parit... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | pureTail_at_end | [188, 1] | [197, 23] | let inq := Nat.le_trans le ineq | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
kw : k < num_clauses
ineq : m β€ k
β’ get' (get' clauses k kw) index bound = none β¨ get' (get' clauses k kw) index bound = some parity | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
kw : k < num_clauses
ineq : m β€ k
inq : num_clauses β€ k := Nat.le_trans le ineq
β’ get' (get' clauses k kw) index bound = none β¨ get' (get' clauses k kw) index bound = some parity | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
kw : k < num_clauses
ineq : m β€ k
β’ get' (get' clauses k kw) index bound = none β¨ get' (get' clauses k kw) index bound = some ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | pureTail_at_end | [188, 1] | [197, 23] | let inq2 := Nat.lt_of_lt_of_le kw inq | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
kw : k < num_clauses
ineq : m β€ k
inq : num_clauses β€ k := Nat.le_trans le ineq
β’ get' (get' clauses k kw) index bound = none β¨ get' (get' clauses k kw) index bound = some parity | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
kw : k < num_clauses
ineq : m β€ k
inq : num_clauses β€ k := Nat.le_trans le ineq
inq2 : k < k := Nat.lt_of_lt_of_le kw inq
β’ get' (get' clauses k kw) index bound = none β¨ get' (get' clause... | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
kw : k < num_clauses
ineq : m β€ k
inq : num_clauses β€ k := Nat.le_trans le ineq
β’ get' (get' clauses k kw) index bound = none ... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Clause.lean | pureTail_at_end | [188, 1] | [197, 23] | exact (False.elim (Nat.lt_irrefl k inq2)) | num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
kw : k < num_clauses
ineq : m β€ k
inq : num_clauses β€ k := Nat.le_trans le ineq
inq2 : k < k := Nat.lt_of_lt_of_le kw inq
β’ get' (get' clauses k kw) index bound = none β¨ get' (get' clause... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
num_clauses n : β
clauses : Vector (Clause n) num_clauses
index : β
bound : index < n
parity : Bool
m : β
le : num_clauses β€ m
k : β
kw : k < num_clauses
ineq : m β€ k
inq : num_clauses β€ k := Nat.le_trans le ineq
inq2 : k < k := Nat.lt_of_lt_of_le kw inq
β’ ge... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | top_of_join_not_positive | [69, 1] | [83, 19] | intro join | bf : Bool
left right top : Option Bool
β’ IsJoin left right top β Β¬left = some bf β Β¬right = some bf β Β¬top = some bf | bf : Bool
left right top : Option Bool
join : IsJoin left right top
β’ Β¬left = some bf β Β¬right = some bf β Β¬top = some bf | Please generate a tactic in lean4 to solve the state.
STATE:
bf : Bool
left right top : Option Bool
β’ IsJoin left right top β Β¬left = some bf β Β¬right = some bf β Β¬top = some bf
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | top_of_join_not_positive | [69, 1] | [83, 19] | induction join with
| noneNone => intros; simp
| noneSome b =>
intros
assumption
| someNone b =>
intros
assumption
| someSome b =>
intros
assumption | bf : Bool
left right top : Option Bool
join : IsJoin left right top
β’ Β¬left = some bf β Β¬right = some bf β Β¬top = some bf | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
bf : Bool
left right top : Option Bool
join : IsJoin left right top
β’ Β¬left = some bf β Β¬right = some bf β Β¬top = some bf
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | top_of_join_not_positive | [69, 1] | [83, 19] | intros | case noneNone
bf : Bool
left right top : Option Bool
β’ Β¬none = some bf β Β¬none = some bf β Β¬none = some bf | case noneNone
bf : Bool
left right top : Option Bool
aβΒΉ aβ : Β¬none = some bf
β’ Β¬none = some bf | Please generate a tactic in lean4 to solve the state.
STATE:
case noneNone
bf : Bool
left right top : Option Bool
β’ Β¬none = some bf β Β¬none = some bf β Β¬none = some bf
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | top_of_join_not_positive | [69, 1] | [83, 19] | simp | case noneNone
bf : Bool
left right top : Option Bool
aβΒΉ aβ : Β¬none = some bf
β’ Β¬none = some bf | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case noneNone
bf : Bool
left right top : Option Bool
aβΒΉ aβ : Β¬none = some bf
β’ Β¬none = some bf
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | top_of_join_not_positive | [69, 1] | [83, 19] | intros | case noneSome
bf : Bool
left right top : Option Bool
b : Bool
β’ Β¬none = some bf β Β¬some b = some bf β Β¬some b = some bf | case noneSome
bf : Bool
left right top : Option Bool
b : Bool
aβΒΉ : Β¬none = some bf
aβ : Β¬some b = some bf
β’ Β¬some b = some bf | Please generate a tactic in lean4 to solve the state.
STATE:
case noneSome
bf : Bool
left right top : Option Bool
b : Bool
β’ Β¬none = some bf β Β¬some b = some bf β Β¬some b = some bf
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | top_of_join_not_positive | [69, 1] | [83, 19] | assumption | case noneSome
bf : Bool
left right top : Option Bool
b : Bool
aβΒΉ : Β¬none = some bf
aβ : Β¬some b = some bf
β’ Β¬some b = some bf | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case noneSome
bf : Bool
left right top : Option Bool
b : Bool
aβΒΉ : Β¬none = some bf
aβ : Β¬some b = some bf
β’ Β¬some b = some bf
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | top_of_join_not_positive | [69, 1] | [83, 19] | intros | case someNone
bf : Bool
left right top : Option Bool
b : Bool
β’ Β¬some b = some bf β Β¬none = some bf β Β¬some b = some bf | case someNone
bf : Bool
left right top : Option Bool
b : Bool
aβΒΉ : Β¬some b = some bf
aβ : Β¬none = some bf
β’ Β¬some b = some bf | Please generate a tactic in lean4 to solve the state.
STATE:
case someNone
bf : Bool
left right top : Option Bool
b : Bool
β’ Β¬some b = some bf β Β¬none = some bf β Β¬some b = some bf
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | top_of_join_not_positive | [69, 1] | [83, 19] | assumption | case someNone
bf : Bool
left right top : Option Bool
b : Bool
aβΒΉ : Β¬some b = some bf
aβ : Β¬none = some bf
β’ Β¬some b = some bf | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case someNone
bf : Bool
left right top : Option Bool
b : Bool
aβΒΉ : Β¬some b = some bf
aβ : Β¬none = some bf
β’ Β¬some b = some bf
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | top_of_join_not_positive | [69, 1] | [83, 19] | intros | case someSome
bf : Bool
left right top : Option Bool
b : Bool
β’ Β¬some b = some bf β Β¬some b = some bf β Β¬some b = some bf | case someSome
bf : Bool
left right top : Option Bool
b : Bool
aβΒΉ aβ : Β¬some b = some bf
β’ Β¬some b = some bf | Please generate a tactic in lean4 to solve the state.
STATE:
case someSome
bf : Bool
left right top : Option Bool
b : Bool
β’ Β¬some b = some bf β Β¬some b = some bf β Β¬some b = some bf
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | top_of_join_not_positive | [69, 1] | [83, 19] | assumption | case someSome
bf : Bool
left right top : Option Bool
b : Bool
aβΒΉ aβ : Β¬some b = some bf
β’ Β¬some b = some bf | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case someSome
bf : Bool
left right top : Option Bool
b : Bool
aβΒΉ aβ : Β¬some b = some bf
β’ Β¬some b = some bf
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | var_resolution_step | [86, 1] | [110, 23] | intro hyp | left right top : Option Bool
join : IsJoin left right top
valuationVal : Bool
β’ VarSat left valuationVal β¨ VarSat right valuationVal β VarSat top valuationVal | left right top : Option Bool
join : IsJoin left right top
valuationVal : Bool
hyp : VarSat left valuationVal β¨ VarSat right valuationVal
β’ VarSat top valuationVal | Please generate a tactic in lean4 to solve the state.
STATE:
left right top : Option Bool
join : IsJoin left right top
valuationVal : Bool
β’ VarSat left valuationVal β¨ VarSat right valuationVal β VarSat top valuationVal
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | var_resolution_step | [86, 1] | [110, 23] | cases hyp with
| inl heq =>
induction join with
| noneNone =>
assumption
| noneSome b =>
injection heq
| someNone b =>
assumption
| someSome b =>
assumption
| inr heq =>
induction join with
| noneNone =>
assumption
| noneSome b =>
assumption
| someNone b =>
injection heq
... | left right top : Option Bool
join : IsJoin left right top
valuationVal : Bool
hyp : VarSat left valuationVal β¨ VarSat right valuationVal
β’ VarSat top valuationVal | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
left right top : Option Bool
join : IsJoin left right top
valuationVal : Bool
hyp : VarSat left valuationVal β¨ VarSat right valuationVal
β’ VarSat top valuationVal
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | var_resolution_step | [86, 1] | [110, 23] | induction join with
| noneNone =>
assumption
| noneSome b =>
injection heq
| someNone b =>
assumption
| someSome b =>
assumption | case inl
left right top : Option Bool
join : IsJoin left right top
valuationVal : Bool
heq : VarSat left valuationVal
β’ VarSat top valuationVal | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
left right top : Option Bool
join : IsJoin left right top
valuationVal : Bool
heq : VarSat left valuationVal
β’ VarSat top valuationVal
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | var_resolution_step | [86, 1] | [110, 23] | assumption | case inl.noneNone
left right top : Option Bool
valuationVal : Bool
heq : VarSat none valuationVal
β’ VarSat none valuationVal | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.noneNone
left right top : Option Bool
valuationVal : Bool
heq : VarSat none valuationVal
β’ VarSat none valuationVal
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | var_resolution_step | [86, 1] | [110, 23] | injection heq | case inl.noneSome
left right top : Option Bool
valuationVal b : Bool
heq : VarSat none valuationVal
β’ VarSat (some b) valuationVal | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.noneSome
left right top : Option Bool
valuationVal b : Bool
heq : VarSat none valuationVal
β’ VarSat (some b) valuationVal
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | var_resolution_step | [86, 1] | [110, 23] | assumption | case inl.someNone
left right top : Option Bool
valuationVal b : Bool
heq : VarSat (some b) valuationVal
β’ VarSat (some b) valuationVal | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.someNone
left right top : Option Bool
valuationVal b : Bool
heq : VarSat (some b) valuationVal
β’ VarSat (some b) valuationVal
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | var_resolution_step | [86, 1] | [110, 23] | assumption | case inl.someSome
left right top : Option Bool
valuationVal b : Bool
heq : VarSat (some b) valuationVal
β’ VarSat (some b) valuationVal | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl.someSome
left right top : Option Bool
valuationVal b : Bool
heq : VarSat (some b) valuationVal
β’ VarSat (some b) valuationVal
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | var_resolution_step | [86, 1] | [110, 23] | induction join with
| noneNone =>
assumption
| noneSome b =>
assumption
| someNone b =>
injection heq
| someSome b =>
assumption | case inr
left right top : Option Bool
join : IsJoin left right top
valuationVal : Bool
heq : VarSat right valuationVal
β’ VarSat top valuationVal | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
left right top : Option Bool
join : IsJoin left right top
valuationVal : Bool
heq : VarSat right valuationVal
β’ VarSat top valuationVal
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | var_resolution_step | [86, 1] | [110, 23] | assumption | case inr.noneNone
left right top : Option Bool
valuationVal : Bool
heq : VarSat none valuationVal
β’ VarSat none valuationVal | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.noneNone
left right top : Option Bool
valuationVal : Bool
heq : VarSat none valuationVal
β’ VarSat none valuationVal
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | var_resolution_step | [86, 1] | [110, 23] | assumption | case inr.noneSome
left right top : Option Bool
valuationVal b : Bool
heq : VarSat (some b) valuationVal
β’ VarSat (some b) valuationVal | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.noneSome
left right top : Option Bool
valuationVal b : Bool
heq : VarSat (some b) valuationVal
β’ VarSat (some b) valuationVal
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | var_resolution_step | [86, 1] | [110, 23] | injection heq | case inr.someNone
left right top : Option Bool
valuationVal b : Bool
heq : VarSat none valuationVal
β’ VarSat (some b) valuationVal | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.someNone
left right top : Option Bool
valuationVal b : Bool
heq : VarSat none valuationVal
β’ VarSat (some b) valuationVal
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | var_resolution_step | [86, 1] | [110, 23] | assumption | case inr.someSome
left right top : Option Bool
valuationVal b : Bool
heq : VarSat (some b) valuationVal
β’ VarSat (some b) valuationVal | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.someSome
left right top : Option Bool
valuationVal b : Bool
heq : VarSat (some b) valuationVal
β’ VarSat (some b) valuationVal
TACTIC:
|
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | have lem1 : left.get' kl llt =
left.get' triple.pivot triple.pivotLt := by
apply witness_independent
apply cc | n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
xβ : ClauseSat right valuation
kr : β
rlt : kr < ... | n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
xβ : ClauseSat right valuation
kr : β
rlt : kr < ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | have lem2 : valuation.get' kl llt =
valuation.get' triple.pivot triple.pivotLt := by
apply witness_independent
apply cc | n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
xβ : ClauseSat right valuation
kr : β
rlt : kr < ... | n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
xβ : ClauseSat right valuation
kr : β
rlt : kr < ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | rw [Vector.get'] at lem1 | n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
xβ : ClauseSat right valuation
kr : β
rlt : kr < ... | n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
xβ : ClauseSat right valuation
kr : β
rlt : kr < ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | have lem3 : some true = some false := by
rw [β c, β lem2, Vector.get', β wl, lem1, triple.leftPivot] | n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
xβ : ClauseSat right valuation
kr : β
rlt : kr < ... | n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
xβ : ClauseSat right valuation
kr : β
rlt : kr < ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | simp at lem3 | n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
xβ : ClauseSat right valuation
kr : β
rlt : kr < ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Resolution.lean | triple_step | [143, 1] | [221, 98] | apply witness_independent | n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
xβ : ClauseSat right valuation
kr : β
rlt : kr < ... | case a
n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isLt := llt })
xβ : ClauseSat right valuation
kr : β
rlt ... | Please generate a tactic in lean4 to solve the state.
STATE:
n : β
left right top : Clause (n + 1)
triple : ResolutionTriple left right top
valuation : Valuation (n + 1)
xβΒΉ : ClauseSat left valuation
kl : β
llt : kl < n + 1
wl : VarSat (Vector.get left { val := kl, isLt := llt }) (Vector.get valuation { val := kl, isL... |
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