Step
*
of Lemma
expfact_wf
No Annotations
∀[m:ℕ+]. ∀[k:ℕ]. ∀[n:ℕ+]. ∀b:{b:ℕ| n * k^b < (b)!} . ((m ≤ b)
⇒ (expfact(m;k;n * k^m;(m)!) ∈ {b:ℕ+| (n * k^b) ≤ (b)!} \000C))
BY
{ ((UnivCD THENA Auto) THEN Assert ⌜∀d:ℕ. (d < b
⇒ (expfact(b - d;k;n * k^(b - d);(b - d)!) ∈ {b:ℕ+| (n * k^b) ≤ (b)!} \000C))⌝⋅) }
1
.....assertion.....
1. m : ℕ+
2. k : ℕ
3. n : ℕ+
4. b : {b:ℕ| n * k^b < (b)!}
5. m ≤ b
⊢ ∀d:ℕ. (d < b
⇒ (expfact(b - d;k;n * k^(b - d);(b - d)!) ∈ {b:ℕ+| (n * k^b) ≤ (b)!} ))
2
1. m : ℕ+
2. k : ℕ
3. n : ℕ+
4. b : {b:ℕ| n * k^b < (b)!}
5. m ≤ b
6. ∀d:ℕ. (d < b
⇒ (expfact(b - d;k;n * k^(b - d);(b - d)!) ∈ {b:ℕ+| (n * k^b) ≤ (b)!} ))
⊢ expfact(m;k;n * k^m;(m)!) ∈ {b:ℕ+| (n * k^b) ≤ (b)!}
Latex:
Latex:
No Annotations
\mforall{}[m:\mBbbN{}\msupplus{}]. \mforall{}[k:\mBbbN{}]. \mforall{}[n:\mBbbN{}\msupplus{}].
\mforall{}b:\{b:\mBbbN{}| n * k\^{}b < (b)!\} . ((m \mleq{} b) {}\mRightarrow{} (expfact(m;k;n * k\^{}m;(m)!) \mmember{} \{b:\mBbbN{}\msupplus{}| (n * k\^{}b) \mleq{} (b)!\} ))
By
Latex:
((UnivCD THENA Auto)
THEN Assert \mkleeneopen{}\mforall{}d:\mBbbN{}. (d < b {}\mRightarrow{} (expfact(b - d;k;n * k\^{}(b - d);(b - d)!) \mmember{} \{b:\mBbbN{}\msupplus{}| (n * k\^{}b) \mleq{} (b)!\} ))\000C\mkleeneclose{}\mcdot{}
)
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