Logic/Logic patterns
A: a, b, 0, 1, +, -, ., /, =, =/=, ~, ().
B: ++ = +, +- = +-, -- = -, +.+ = +, +/+ = +, -.- = +, -/- = +, +.- = -, +/- = -, -/+ = -
C: + = + , - = -, . = ., / = /, ~ = ~, = = =, =/= = =/=, () = ()
D: + =/= -, . =/= /, ~ =/= -, = =/= =/=
E: =
1. a => a <=> a = a
2. ~a => ~a <=> ~a = ~a
3. a =/=> ~a <=> a =/= ~a
4. a ^ ɸ => a <=> a + 0 = a
5. a ^ ~ɸ => a <=> a - 0 = a
6. ~a ^ ɸ => ~a <=> ~a + 0 = ~a
7. ~a ^ ~ɸ => ~a <=> ~a - 0 = ~a
8. a v 1 => a <=> a.1 = a
9. a < 1 => a <=> a/1 = a
10. ~a v 1 => ~a <=> ~a.1 = ~a
11. ~a < 1 => ~a <=> ~a/1 = ~a
12. a v ɸ => ɸ <=> a.0 = 0
13. a < ɸ => ɸ <=> a/0 = 0
14. ~a v ɸ => ɸ <=> ~a.0 = 0
15. ~a < ɸ => ɸ <=> ~a/0 = 0
16. a ^ 1 => 1 ^ a <=> a + 1 = 1 + a
17. a ^ ~1 => Q ^ a <=> a - 1 = -1 + a
18. ~a ^ 1 => 1 ^ ~a <=> ~a + 1 = 1 + ~a
19. ~a ^ ~1 => Q ^ ~a <=> ~a - 1 = -1 + ~a
20. ɸ ^ a => a <=> 0 + a = a
21. ɸ ^ ~a => ~a <=> 0 - a = -a
22. ɸ ^ ~(~a) => !a <=> 0 - ~a = - ~a
23. a ^ a => a ^ a <=> a + a = a + a
24. a v a => a <=> a . a = a
25. a ^ ~a => e <=> a - a = 0
26. a < a => 1 <=> a / a = 1
27. a v ~a => Q <=> a . ~a = 0
28. a ^ ~(~a) => a ^ !a <=> a - ~a = 1
29. a < ~a => Q <=> a / ~a = -1
30. a v b => b v a <=> a . b = b . a
31. a ^ b => b ^ a <=> a + b = b + a
32. (a ^ b) ^ c => a ^ (b ^ c) <=> (a + b) + c = a + (b + c)
33. (a v b) v c => a v (b v c) <=> (a . b) . c = a . (b . c)
34. a ^ (b v c) => (a ^ b) v (a ^ c) <=> a + (b . c) = (a + b) . (a + c)
35. a v (b ^ c) => (a v b) ^ (a v c) <=> a . (b + c) = (a . b) + (a . c)
36. ~(a ^ b) => ~a ^ ~b <=> ~(a + b) = ~a + ~b
37. ~(a v b) => ~a v ~b <=> ~(a . b) = ~a . ~b
38. a < b => a < b <=> a / b = a / b
39. a ^ ~b => ~b ^ a <=> a - b = -b + a
40. (a ^ ~b) ^ ~c => a ^ (~b ^ ~c) <=> (a - b) - c = a (-b - c)
41.i.(a < b) < c => a < (b v c) <=> (a / b) / c = a / (b . c)
41.ii. a < (b < c) => (a v c) < b <=> a / (b / c) = (a . c) / b
42. a ^ ~(b < c) => (a ^ ~b) < (a ^ ~c) <=> a - (b / c) = (a - b) / (a - c)
43. a < (b ^ ~c) => (a < b) ^ ~(a < c) <=> a / (b - c) = (a / b) - (a / c)
44. ~(a ^ ~b) => ~a ^ ~(~b) <=> ~(a - b) = ~a - ~b
45. ~(a < b) => ~a < ~b <=> ~(a / b) = ~a / ~b
46. ʘ => ʒ ^ e
47. ψa => a ^ ~a ^ !a
48. Эa => a v ~a v !a
49. ʒ => e
50. ɸ => ʒ ^ ~e
51. 1 => a < a
52. e => a ^ ~a
53. Q => ~ɸ ^ ~1
54. !a => ~(~a)
55. ʘ => ʒ ^ e < (Q ^ !e) v [(ɸ ^ 1) ^ (ψ ^ Э)]
zi': 0 + 0 = 0 <=> ɸ ^ ɸ => ɸ
zi": 0 - 0 = 0 <=> ɸ ^ ~ɸ => Q
zi"': 0 . 0 = 0 <=> ɸ v ɸ => ɸ
zi"": 0 / 0 = 0 <=> ɸ < ɸ => ∞
zii':0 . 1 = 0 <=> ɸ v 1 => ɸ
zii": 1 . 0 = 0 <=> 1 v ɸ => ɸ
zii"': 0 / 1 = 0 <=> ɸ < 1 => ɸ
zii"": 1 / 0 = 0 <=> 1 < ɸ => ɸ
ziii': 0 . a = 0 <=> ɸ v a => ɸ
ziii": a . 0 = 0 <=> a v ɸ => ɸ
ziii"': 0 / a = 0 <=> ɸ < a => ɸ
ziii"": a / 0 = 0 <=> a < ɸ => ɸ
ziv': 0 . ~a = 0 <=> ɸ v ~a => ɸ
ziv": ~a . 0 = 0 <=> ~a v ɸ => ɸ
ziv"': 0 / ~a = 0 <=> ɸ < ~a => ɸ
ziv"": ~a / 0 = 0 <=> ~a < ɸ => ɸ
zv': 1 - 1 = 0 <=> 1 ^ ~1 => Q
zv": a - a = 0 <=> a ^ ~a => e
zv"': ~a - ~a = 0 <=> ~a ^ ~(~a) => !ɸ
zv"": a + ~a = 0 <=> a ^ ~a => e
G1. ЭX < ЭY
G2. ЭX < Э~Y
G3. ЭY < ЭX
G4. ЭY < Э~X
G5. Э~X < ЭY
G6. Э~Y < ЭX
G7. Э~X < Э~Y
G8. Э~Y < Э~X
G9. [~]X < ЭY
G10. [~]Y < ЭX
G11. [~]Y < Э~X
G12. [~]~X < ЭY
G13. [~]X < Э~Y
G14. [~]~Y < ЭX
G15. [~]~X < ~Y
G16. [~]~Y < ~X
P1. (ЭX < ЭY) ^ ([~]Y < Э~X) => (ЭX < ψY)
P2. (ЭX < Э~Y) ^ ([~]X < ЭY) => (ψX < Э~Y)
P3. (ЭX < ЭY) ^ (ЭY < ЭX) => (ЭX < ЭY)
P4. (Э~X < ЭY) ^ (ЭY < Э~X) => (Э~X < ЭY)
One.
1. (ψB < ~A) => (ψA < ~B)
2. (ЭA < ψC) ^ (ЭC < ЭB) =/=> [(ψB < ~A) <= (ЭC < ЭB)]
3. (ψB < ЭA) => (ЭA < ψB)
4. (ψA < ~B) => (ψB < ~A)
5. (ψB < ЭA)
6. (ЭB < ЭA) => (ЭA < ЭB)
7. (ψA < ~B) => (ψB < ~A)
8. (ЭB < ~A) => [(ЭA < ЭB) v (ψA < ~B)]
Two.
1. (ЭA < ψB) ^ (ЭB < ψC) => (ЭA < ψC)
2. (ψA < ~B) ^ (ЭB < ψC) => (ψA < ~C)
Three.
1. (ψB < ЭA) ^ (ЭC < ЭB) => (ЭC < ЭA)
2. (ψB < ~A) ^ (ЭC < ЭB) => (ЭC < ~A)
Four.
1. (ψA < ~B) ^ (ЭA < ψC)
2. (ψA < ~B) <=> (ψB < ~A) <= [(ψ < ~) <=> (~ < ψ)]
3. (ЭA < ψC)
4. (ψB < ~C)
5. (ЭA < ψB) ^ (ψA < ~C) => (ψB < ~C)
6. (ψA < ~C) => (ψC < ~A)
7. (ЭA < ψB)
8. (ψC < ~B)
9. (ψC < ~B) => (ψB < ~C)
Five.
1. (ψA < ~B) ^ (ЭA < ЭC) => (ЭC < ~B)
2. [(ψA < ~B) => (ψB < ~A)] <= [(ψ < ~) <=> (~ < ψ)]
3. (ЭA < ЭC)
4. (ЭC < ~B)
5. (ЭA < ψB) ^ (ψA < ~C) => (ψB < ~C)
6. (ЭB < ψC) ^ (ЭA < ψB) => (ЭA < ψC)
7. (ψA < ~C)
8. (ЭA < ψB) ^ (ЭC < ~A) => (ЭC < ~B)
Six.
1. (ЭA < ψB) ^ (ЭA < ЭC)
2. (ЭB < ψC) v (ψB < ~C)
3. (ψA < ~C) ^ (ЭA < ~B)
4. (ЭB < ψC) v (ψB < ~C)
Seven.
1. (ЭA < ψC) ^ (ЭB < ψC) => (ЭA < ЭB)
2. [(ЭB < ψC) <=> (ψC < ЭB)] <= [(Э < ψ) <=> (ψ < Э)]
3. (ЭA < ψC) ^ (ψC < ЭB) => (ЭA < ЭB)
Eight.
1. [(ЭA < ψC) ^ (ЭB < ψC)] ^ (ЭC < ψD)
2. [(ЭA < ψD) ^ (ЭB < ψD)] => (ЭA < ЭB)
3. (ЭB < ψC) ^ (ψA < ~C) => (ЭB < ~A)
Nine.
1. (ЭB < ψC) ^ (ЭA < ЭC) => (ЭA < ЭB)
2. [(ЭA < ЭC) <=> (ЭC < ЭA)] <= [(Э < Э) <=> (Э < Э)]
3. (ЭB < ψC) ^ (ЭC < ЭA) => (ЭB < ЭA)]
4. (ЭA < ЭB)]
Ten.
1. (ЭB < ЭC) ^ (ЭA < ψC) => (ЭA < ЭB)
2. (ЭB < ψC) ^ (ЭA < ~C) => (ЭA < ~B)
3. (ЭA < ψB) ^ (ЭB < ψC) => (ЭA < ψC)
4. (ЭA < ~C)
Eleven.
1. (ψA < ~C) ^ (ЭB < ЭC) => (ЭA < ~B)
Twelve.
1. [(ЭA < ψB) v (ЭA < ЭB)] ^ (ψB < ~C)
2. [(ψB < ЭA) v (ЭB < ЭA)] ^ (ψC < ~B)
3. (ЭA < ~C)
Thirteen.
1. (ЭA < ψC) ^ (ЭB < ψC) => (ЭA < ЭB)
2. (ψA < ~B) ^ (ЭB < ψC) => (ψA < ~C)
3. (ЭA < ψC)
Fourteen.
1. (ЭA < ψB) ^ (ЭB < ЭC) => (ЭA < ЭC)
2. (ψA < ~C) ^ (ЭA < ψB) => (ψB < ~C)
3. (ψA < ~B) ^ (ЭB < ЭC) => (ЭC < ~A)
4. (ЭA < ψC) ^ (ψA < ~B) => (ψB < ~C)
Fifteen.
1. (ЭA < ψB) ^ (ЭB < ЭC)
2. (ЭA < ЭC)
3. (ЭB < ЭC) ^ (ЭA < ψB)
Sixteen.
1. (ψB < ~A) ^ (ЭA < ψC)
2. [(ψB < ~A) => (ψA < ~B)] <= [(ψ < ~) => (~ < ψ)]
3. (ЭA < ψC)
4. (ψB < ~C)
5. (ψC < ЭA)
Seventeen.
1. (ψA < ~C) => (ψC < ~A)
2. (ЭA < ψB)
3. (ψC < ~B)
4. (ψB < ~C)
Eighteen.
1. (ψC < ~A)
2. (ψB < ~C) => (ψC < ~B)
3. (ЭB < ЭA) <= (ЭA < ψB)
4.(ψC < ~A)
Nineteen.
1. (ψB < ~A) ^ (ЭC < ЭA)
2. (ψB < ~A) => (ψA < ~B)
3. (ЭC < ЭA)
4. (ЭB < ~C)
Twenty.
1. (ЭA < ψB) ^(ЭC < ~A) => (ЭC < ~B)
Twenty One.
1. (ЭA < ψC) ^ (ЭB < ψC)
2. [(ЭB < ψC) => (ЭC < ЭB)] <= [(Э < ψ) => (Э < Э)]
3. (ЭA < ψC) ^ (ЭC < ЭB) => (ЭA < ЭB)
4. (ЭC < ЭB)
Twenty Two.
1. (ЭC < ЭA) => (ЭA < ЭC)
2. (ЭB < ψC) => (ЭB < ЭA)
Twenty Three.
1. (ψA < ~C) ^ (ЭB < ЭC)
2. (ЭB < ЭC) ^ (ψA < ~C) => (ЭA < ~B)
3. (ЭB < ЭC)
Twenty Four.
1. (ЭB < ЭC) ^ (ψA < ~C)
2. (ЭB < ЭC) => (ЭC < ЭB)
3. (ψA < ~C) ^ (ЭB < ЭC) => (ЭA < ~B)
Twenty Five.
1. (ЭB < ψC) ^ (ЭA < ЭC) => (ЭB < ЭA)
2. (ψA < ~C) ^ (ЭB < ЭC) => (ЭB < ~A)
Twenty Six.
1. [(ЭA < ψB) v (ЭA < ЭB)] ^ (ЭB < ψC)
2. (ЭA < ψC) v (ЭA < ЭC)
3. [(ψA < ~B) v (ЭA < ~B)] ^ (ЭB < ψC)
4. (ψA < ~C) v (ЭA < ~C)
5. {[(ЭA < ψB) v (ЭA < ЭB)] ^ (ЭB < ЭC)} => [(ЭA < ψC) v (ЭA < ЭC)]
Twenty Seven.
1. {[(ψA < ~B) v (ЭA < ~B)] ^ (ЭB < ЭC)} => [(ψA < ~C) v (ЭA < ~C)]
Twenty Eight.
1. [(ЭA < ψB) v (ЭA < ЭB)] ^ (ЭB < ψC)
2. {(ЭB < ψC) ^ [(ЭA < ψB) v (ЭA < ЭB)]} => [(ЭA < ψC) v (ЭA < ЭC)]
Twenty Nine.
1. {[(ψA < ~B) v (ЭA < ~B)] ^ (ЭB < ψC )} => [(ψA < ~C) v (ЭA < ~C)]
Thirty.
1. A < B
2. [(A <= B) v (A => B v ~B)] ^ (~A => ~B)
3. (A v ~A) ^ ~B
4. (A v ~A) => (A v ~A)
5. ~B => ~B
6. (A v ~A) ^ ~B
7. [(A ^ ~B) v (~A ^ ~B)] => [(A < A) ^ (A => A)]
8. (A => A) <=> (A < A)
Thirty One.
1. (A v ~A) ^ (A < B) => [(A => B) v (~A => ~B)]
2. A <= B
3. {[(A => B v ~B) v (~A => ~B)] ^ (A v ~A)} => (B v ~B)
4. (~B v ~B) => [(~B v ~B) ^ (B v ~B)]
Thirty Two.
1. (~B v ~B) ^ ~(B v B) ^ ~(ψB v ЭB)
2. (ЭB < ψC)
3. (ψA < ~C) ^ (ЭB < ψC) => [(ЭA < ~B) v (ψA < ~B)]
4. (ЭA < ψB) v (ЭA < ЭB)
5. (ЭA < ψC) v (ЭA < ЭC)
6. (ψA < ~C) <=/=> [(ЭA < ψC) v (ЭA < ЭC)]
Thirty Three.
1. B < C
2. {(ЭB < ψC) ^ [(ЭA < ψB) v (ЭA < ЭB)]} => [(ЭA < ψC) v (ЭA < ЭC)]
3. (ψA < ~C) v (ЭA < ~C)
Thirty Four.
1. (ψA < ~B) ^ [(ЭB < ψC) v (ЭB < ЭC)]
2. (ЭA < ~C) v (ψA < ~C)
3. (ψA < ~C) ^ [(ЭB < ψC) v (ЭB < ЭC)]
4. (ЭA < ЭB)
5. (ψA < ~B) <=/=> (ЭA < ЭB)
6. (ψA < ~C)
Thirty Five.
1. (ЭA < ψB) ^ [(ψB < ~C) v (ЭB < ~C)]
2. (ЭA < ~C) v (ЭA < ~C)
3. (ЭB < ψC) v (ЭB < ЭC)
4. {(ЭA < ψB) ^ [(ЭB < ψC) v (ЭB < ЭC)]} => [(ЭA < ψC) v (ЭA < ЭC)]
Thirty Six.
1. (ψA < ~B) ^ [(ЭB < ~C) v (ψB < ~C)]
2. [(ЭA < ψC) v (ЭA < ЭC)] v [(ЭA < ~C) v (ψA < ~C)]
3. {(ЭA < ψB) ^ [(ЭB < ~C) v (ψB < ~C)]} => [(ЭA < ~C) v (ψA < ~C)]
Thirty Seven.
1. (ψA < ~B) ^ [(ЭB < ~C) v (ψB < ~C)]
2. [(ЭA < ψC) v (ЭA < ЭC)] v [(ЭA < ~C) v (ψA < ~C)]
3. {[(ЭB < ψC) v (ЭB < ЭC)] ^ (ψA < ~B)} => [(ЭA < ~C) v (ψA < ~C)]
Thirty Eight.
1. (ЭA < ψB) ^ [(ЭB < ψC) v (ЭB < ЭC)]
2. [(ЭA < ψC) v (ЭA < ЭC)]
Thirty Nine.
1. [(ЭA < ψB) v (ЭA < ЭB)] ^ (ЭB < ψC)
2. [(ЭA < ЭC) v (ЭA < ψC)] =/=> (ЭA < ψC)]
Forty.
1. (ψB < ~A) ^ [(ЭB < ЭC) v (ЭB < ψC)]
2. (ψA < ~C)
3. [(ЭA < ЭC) v (ЭA < ψC)]
4. (ψB < ~A)
5. (ψB < ~A) => (ψA < ~B)
6. [(ЭA < ЭC) v (ЭA < ψC)]
7. [(ЭB < ~C) v (ψB < ~C)]
8. [(ЭB < ЭC) v (ЭB < ψC)]
Forty One.
1. (ψB < ~A) ^ [(ЭB < ЭC) v (ЭB < ψC)]
2. (ЭA < ~C)
3. (ЭA < ψC) ^ [(ψB < ~A) => (ψA < ~B)]
4. (ЭA < ψC) => (ψC < ~B)
5. [(ЭB < ЭC) v (ЭB < ψC)]
Forty Two.
1. (ψA < ~B) ^ (ЭA < ψC)
2. (ψA < ~B) => (ψB < ~A)
3. (ЭA < ψC)
4. (ψB < ~A) ^ (ЭA < ψC) => (ψB < ~C)
Forty Three.
1. (ψB < ~A) ^ [(ЭA < ψC) v (ЭA < ЭC)]
2. (ψB < ~A) => (ψA < ~B)
3. [(ЭA < ψC) v (ЭA < ЭC)]
4. {(ψA < ~B) ^ [(ЭA < ψC) v (ЭA < ЭC)]} => [(ψC < ~B) v (ЭC < ~B)]
5. (ψC < ~B)
6. (ЭC < ЭB)
7. (ψA < ~B) ^ (ЭC < ЭB) => (ЭA < ~C)
8. [(ЭA < ψC) v (ЭA < ЭC)]
Forty Four.
1. (ψB < ~A) ^ [(ψC < ~A) v (ЭC < ~A) v (ЭC < ЭA)]
2. (ψB < ~A) => (ψA < ~B)
3. (ЭA < ψC)
4. (ψA < ~B) ^ (ЭA < ψC) => (ψB < ~C)
Forty Five.
1. [(ЭA < ψC) v (ЭA < ЭC)] ^ [(ЭB < ψC) v (ЭB < ЭC)]
2. [(ЭB < ψC) v (ЭB < ЭC)] => [ψC < ЭB) v (ЭC < ЭB)]
3. [(ЭA < ψC) v (ЭA < ЭC)] ^ [ψC < ЭB) v (ЭC < ЭB)]
4. (ЭA < ЭB) v (ψA < ~B)
Forty Six.
1. [(ψC < ~A) v (ЭC < ЭA)] ^ [(ЭB < ψC) v (ЭB < ЭC)]
2. (ЭB < ~A) v (ЭB < ЭA)
Forty Seven.
1. [(ψC < ~A) v (ЭC < ~A)] ^ [(ψC < ~B) v (ЭC < ~B)]
2. [(ψB < ~A) v (ЭB < ~A)] v [(ЭB < ψA) v (ЭB < ЭA)]
3. {[(ЭA < ψC) v (ЭA < ЭC)] ^ [(ЭB < ψC) v (ЭB < ЭC)]} => [(ЭB < ψA) v (ЭB < ЭA)]
Forty Eight.
1. [(ЭA < ψC) v (ЭA < ЭC)] ^ (ЭB < ЭC)
2. (ЭB < ЭC) => (ЭC < ЭB)]
3. {[(ЭA < ψC) v (ЭA < ЭC)] ^ (ЭC < ЭB)} => [(ЭA < ЭB) v (ЭA < ~B)]
Forty Nine.
1. (ЭA < ψC) ^ [(ЭB < ψC) v (ψB < ~C)]
2. [(ЭB < ψC) v (ψB < ~C)] => [(ψC < ЭB) v (ψC < ~B)]
3. {(ЭA < ψC) ^ [(ψC < ЭB) v (ψC < ~B)]} => [(ЭA < ЭB) v (ЭA < ~B)]
Fifty.
1. (ЭB < ψC) ^ [(ЭA < ЭC) v (ЭA < ~C)]
2. [(ЭA < ЭB) v (ЭA < ~B)]
3. (ЭA < ψB) ^ (ЭB < ψC)
4. (ЭA < ψC)
5. [(ЭA < ЭC) v (ЭA < ~C)]
Fifty One.
1. (ЭA < ψC) ^ [(ЭB < ψC) v (ЭB < ЭC)]
2. (ЭA < ψC) ^ [(ЭC < ЭB) v (ψC < ЭB)]
3. [(ЭB < ψA) v (ЭB < ЭA)]
Fifty Two.
1. A=>B, C=>A, D=/=>A.
2. E=>F, G=>E, H=/=>E.
3. C <=> F => ЭA < ψE.
4. (ЭF < ψE) ^ (ЭA < ψC) => (ЭA < ψE)
5. [(C <=> G) => (ЭA < ЭE)] <= [(C=>A) ^ (G=>E)]
6. (F <=> D) => (ψA < ~E)
7.{[(ψA < ~E) => (ψE < ~A)] ^ (F <=> D)} => [(ψA < ~F) ^ (ЭF < ψE)].
Fifty Three.
1. (B <=> H) => (ψA < ~E).
2. (ЭB < ψA) ^ (ψB < ~E).
3. (B <=> H) ^ (ψH < ~E).
Fifty Four.
1. (D <=> G) => [(ψA v ЭA) < ~E.]
2. (ψA < ~G) <= (ψA < ~D).
3. ψG < ЭE.
4. (ψA v ЭA) < ~E.
Fifty Five.
1. (B <=> G).
2. (ЭE < ψA) <= {[(ψB < ЭA) ^ (ψE < ЭB)] ^ (B <=> G)}.
3. (ЭA < ψE) v (ЭA < ЭE).
4. (ЭA < ЭE) <= (ψ => Э)
5. (ЭC <=> ЭF) => (ЭA < ψE)
Fifty Six.
1. (C <=> G) => (ЭA <=> ЭE)
2. (ЭD <=> ЭF) => (ψA < ~E)
3. [(ψA < ~F) <= {(ψF < ~A)] ^ (ЭF < ψE)}
4. (ψD < ~A) ^ (ЭD < ψE)
5. (ЭD <=> ЭG) => (ψA < ~E)
6. (ψA < ~G) ^ (ЭE < ψG)
S1. (ЭC < ψB) ^ (ЭB < ψA) => (ЭC < ψA)
S2. (ψC < ~B) ^ (ЭB < ψA) => (ψC < ~A)
S3. (ЭC < ψB) ^ (ЭB < ЭA) => (ЭC < ЭA)
S4. (ψC < ~B) ^ (ЭB < ЭA) => (~C < ЭA)
S5. (ψB < ~C) ^ (ЭB < ψA) => (ψC < ~A)
S6. (ЭB < ψC) ^ (ψB < ~A) => (ψC < ~A)
S7. (ψB < ~C) ^ (ЭB < ЭA) => (~C < ЭA)
S8. (ЭB < ψC) ^ (~B < ЭA) => (~C < ЭA)
S9. (ЭC < ψB) ^ (ЭA < ψB) => (ЭC < ЭA)
S10. (ψC < ~B) ^ (ЭA < ψB) => (~C < ЭA)
S11. (ЭC < ЭB) ^ (ЭA < ψB) => (ЭC < ЭA)
S12. (ЭC < ψB) ^ (ЭA < ЭB) => (ЭC < ЭA)
S13. (~C < ЭB) ^ (ЭA < ψB) => (~C < ЭA)
S14. (ψC < ~B) ^ (ЭA < ЭB) => (~C < ЭA)
S15.(ЭB < ψC) ^ (ЭA < ψB) => (ψC < ЭA)
S16.(ЭB < ψC) ^ (ψA < ~B) => (~C < ψA)
S17.(ЭB < ЭC) ^ (ЭA < ψB) => (ЭC < ЭA)
S18.(ψB < ~C) ^ (ЭA < ψB) => (~C < ЭA)
S19.(ψB < ~C) ^ (ЭA < ЭB) => (~C < ЭA)
1. (ЭC < ψA)
1.1 (ЭC < ψB) ^ (ЭB < ψA)
2. (ψC < ~A)
2.1 (ψC < ~B) ^ (ЭB < ψA)
2.2 (ψB < ~C) ^ (ЭB < ψA)
2.3 (ЭB < ψC) ^ (ψB < ~A)
3. (ЭC < ЭA)
3.1 (ЭC < ψB) ^ (ЭB < ЭA)
3.2 (ЭC < ψB) ^ (ЭA < ψB)
3.3 (ЭC < ψB) ^ (ЭA < ЭB)
3.4 (ЭC < ЭB) ^ (ЭA < ψB)
3.5 (ЭB < ψC) ^ (ЭA < ψB)
3.6 (ЭB < ЭC) ^ (ЭA < ψB)
4.(~C < ЭA)
4.1 (ψC < ~B) ^ (ЭB < ЭA)
4.2 (ψB < ~C) ^ (ЭB < ЭA)
4.3 (ЭB < ψC) ^ (~B < ЭA)
4.4 (ψC < ~B) ^ (ЭA < ψB)
4.5 (~C < ЭB) ^ (ЭA < ψB)
4.6 (ψC < ~B) ^ (ЭA < ЭB)
4.7 (ЭB < ψC) ^ (ψA < ~B)
4.8 (ψB < ~C) ^ (ЭA < ψB)
4.9 (ψB < ~C) ^ (ЭA < ЭB)
Corrections to the original article will be notified here.
Adjustive corrections have since been made to: 41, giving 41.i, 41.ii. Adjustive corrections have also been made to S15 and S16.
See also:
https://en.wikiversity.org/w/index.php?title=User:Shadowjack/Deductive_logic&oldid=1129397
https://en.wikiversity.org/w/index.php?title=User:Glimmerguard/Quantum_Indefinite&oldid=1127754
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