Step
*
2
2
of Lemma
lg-all-remove
1. [T] : Type
2. [P] : T ─→ ℙ
3. g : LabeledGraph(T)@i
4. x : ℕlg-size(g)@i
5. ∀n:ℕlg-size(lg-remove(g;x)). P[lg-label2(lg-remove(g;x);n)]@i
6. P[lg-label2(g;x)]@i
7. n : ℕlg-size(g)@i
8. ¬n < x
⊢ P[lg-label2(g;n)]
BY
{ (Decide x < n THENA Auto)⋅ }
1
1. [T] : Type
2. [P] : T ─→ ℙ
3. g : LabeledGraph(T)@i
4. x : ℕlg-size(g)@i
5. ∀n:ℕlg-size(lg-remove(g;x)). P[lg-label2(lg-remove(g;x);n)]@i
6. P[lg-label2(g;x)]@i
7. n : ℕlg-size(g)@i
8. ¬n < x
9. x < n
⊢ P[lg-label2(g;n)]
2
1. [T] : Type
2. [P] : T ─→ ℙ
3. g : LabeledGraph(T)@i
4. x : ℕlg-size(g)@i
5. ∀n:ℕlg-size(lg-remove(g;x)). P[lg-label2(lg-remove(g;x);n)]@i
6. P[lg-label2(g;x)]@i
7. n : ℕlg-size(g)@i
8. ¬n < x
9. ¬x < n
⊢ P[lg-label2(g;n)]
Latex:
Latex:
1. [T] : Type
2. [P] : T {}\mrightarrow{} \mBbbP{}
3. g : LabeledGraph(T)@i
4. x : \mBbbN{}lg-size(g)@i
5. \mforall{}n:\mBbbN{}lg-size(lg-remove(g;x)). P[lg-label2(lg-remove(g;x);n)]@i
6. P[lg-label2(g;x)]@i
7. n : \mBbbN{}lg-size(g)@i
8. \mneg{}n < x
\mvdash{} P[lg-label2(g;n)]
By
Latex:
(Decide x < n THENA Auto)\mcdot{}
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