Step
*
1
2
of Lemma
empty-bag-union
1. T : Type
2. bs : bag(bag(T))
3. bag-union(bs) = {} ∈ bag(T)
4. ∀bs:Top List List. ((concat(bs) = [] ∈ (Top List))
⇒ (bs ~ bag-rep(||bs||;[])))
⊢ bs ~ bag-rep(#(bs);{})
BY
{ (Unfolds ``bag-size empty-bag`` 0 THEN With ⌜bs⌝ (D (-1))⋅) }
1
.....wf.....
1. T : Type
2. bs : bag(bag(T))
3. bag-union(bs) = {} ∈ bag(T)
⊢ bs ∈ Top List List
2
1. T : Type
2. bs : bag(bag(T))
3. bag-union(bs) = {} ∈ bag(T)
4. (concat(bs) = [] ∈ (Top List))
⇒ (bs ~ bag-rep(||bs||;[]))
⊢ bs ~ bag-rep(||bs||;[])
Latex:
Latex:
1. T : Type
2. bs : bag(bag(T))
3. bag-union(bs) = \{\}
4. \mforall{}bs:Top List List. ((concat(bs) = []) {}\mRightarrow{} (bs \msim{} bag-rep(||bs||;[])))
\mvdash{} bs \msim{} bag-rep(\#(bs);\{\})
By
Latex:
(Unfolds ``bag-size empty-bag`` 0 THEN With \mkleeneopen{}bs\mkleeneclose{} (D (-1))\mcdot{})
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