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Theorem union-split2
h0 ⊥ h1, h2 ⊥ h3 ⊦ h0 ∪ h1 = h2 ∪ h3 ↔ (∃ h20, h21, h30, h31. h2 = h20 ∪ h21 ∧ h3 = h30 ∪ h31 ∧ h0 = h20 ∪ h30 ∧ h1 = h21 ∪ h31 ∧ h20 ⊥ h21 ∧ h30 ⊥ h31 ∧ h20 ⊥ h1 ∧ h30 ⊥ h1 ∧ h21 ⊥ h0 ∧ h31 ⊥ h0)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
union-split3
,
Used by units in proved state:
Proof exists?: Yes
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the proof
Infos about the proof
Proved?: Yes
Interactions: 59
Proof steps: 100
Used lemmas:
uni-ac3-true
,
uni-inj
,
uni-ass
,
disj
,
disj-l
,
disj-diffb
,
disj-com-rw
,
uni-com
,
diff-at
,
at-uni
,
disj-r
,
diff-in
,
subset-union
,
disj-union-diff
,
in-uni
,
disj-distr-uni
,
disj-distr-uni-com
,
Used spec theorems:
map
/
Extension
map
/
notmemlookup
Used simplifier rules: