Step
*
2
of Lemma
mu-dec-property
1. A : Type
2. P : A ⟶ ℕ ⟶ ℙ
3. d : a:A ⟶ k:ℕ ⟶ (P[a;k] + (¬P[a;k]))@i
4. a : A@i
5. ∃k:ℕ. P[a;k]@i
6. mu-dec(d;a) ∈ ℕ
7. P[a;mu-dec(d;a)]
8. i : ℕmu-dec(d;a)@i
9. ↑isl(d a mu-dec(d;a))
10. ∀[i:ℕ]. ¬↑isl(d a i) supposing i < mu-dec(d;a)
11. ¬↑isl(d a i)
⊢ ¬P[a;i]
BY
{ OnMaybeHyp 11 (\h. (MoveToConcl h THEN GenConclAtAddr [1;1;1;1] THEN D -2 THEN Reduce 0 THEN Complete (Auto))⋅) }
Latex:
Latex:
1. A : Type
2. P : A {}\mrightarrow{} \mBbbN{} {}\mrightarrow{} \mBbbP{}
3. d : a:A {}\mrightarrow{} k:\mBbbN{} {}\mrightarrow{} (P[a;k] + (\mneg{}P[a;k]))@i
4. a : A@i
5. \mexists{}k:\mBbbN{}. P[a;k]@i
6. mu-dec(d;a) \mmember{} \mBbbN{}
7. P[a;mu-dec(d;a)]
8. i : \mBbbN{}mu-dec(d;a)@i
9. \muparrow{}isl(d a mu-dec(d;a))
10. \mforall{}[i:\mBbbN{}]. \mneg{}\muparrow{}isl(d a i) supposing i < mu-dec(d;a)
11. \mneg{}\muparrow{}isl(d a i)
\mvdash{} \mneg{}P[a;i]
By
Latex:
OnMaybeHyp 11 (\mbackslash{}h. (MoveToConcl h
THEN GenConclAtAddr [1;1;1;1]
THEN D -2
THEN Reduce 0
THEN Complete (Auto))\mcdot{})
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