Step
*
1
of Lemma
word-rel-append1
1. X : Type
2. w1 : (X + X) List
3. x : (X + X) List
4. y : (X + X) List
5. x@0 : X + X
6. y@0 : X + X
7. a : (X + X) List
8. b : (X + X) List
9. x@0 = -y@0
10. x = (a @ [x@0; y@0] @ b) ∈ ((X + X) List)
11. y = (a @ b) ∈ ((X + X) List)
⊢ ∃b:(X + X) List
(x@0 = -y@0 ∧ ((x @ w1) = (a @ [x@0; y@0] @ b) ∈ ((X + X) List)) ∧ ((y @ w1) = (a @ b) ∈ ((X + X) List)))
BY
{ (D 0 With ⌜b @ w1⌝ THEN Auto THEN RWO "-3" 0 THEN Auto) }
Latex:
Latex:
1. X : Type
2. w1 : (X + X) List
3. x : (X + X) List
4. y : (X + X) List
5. x@0 : X + X
6. y@0 : X + X
7. a : (X + X) List
8. b : (X + X) List
9. x@0 = -y@0
10. x = (a @ [x@0; y@0] @ b)
11. y = (a @ b)
\mvdash{} \mexists{}b:(X + X) List. (x@0 = -y@0 \mwedge{} ((x @ w1) = (a @ [x@0; y@0] @ b)) \mwedge{} ((y @ w1) = (a @ b)))
By
Latex:
(D 0 With \mkleeneopen{}b @ w1\mkleeneclose{} THEN Auto THEN RWO "-3" 0 THEN Auto)
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