logic - 惠誉风格证明

Question

嗨，我在解决Fitch Style Proof时遇到了麻烦，希望有人能帮助我。

前提:

A ^ (B v C)
B => D
C => E

目标:

~E => D

Answer 1

(1)   A /\ (B \/ C)  premise
(2)   B -> D         premise
(3)   C -> E         premise
     .--------------------------------------------.
(4)  | ~E            assumption                   |
(5)  | B \/ C        /\ elimination of 1          |
     | .--------------------------------------.   |
(6)  | | B          assumption                |   |
(7)  | | D          -> elimination 2          |   |
     | '--------------------------------------'   |
     | .--------------------------------------.   |
(8)  | | C          assumption                |   |
(9)  | | E          -> elimination 3          |   |
(10) | | cont       contradiction             |   |
(11) | | D          ! elimination 10          |   |
     | '--------------------------------------'   |
(12) |  D           \/ elimination 5, 6-7, 8-11   |
     '--------------------------------------------'
(13) ~E -> D        -> introduction 4-12