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Signature symbols in this unit

Symbol Specification Kind Type
# .mapfMap[A, B] → Nat
# .set-basicfSet[A] → Nat
# .treefTree[A] → Nat
. ( . )mappfMap[A, B] × A → B with λ st, a. a ∈ st
. ( . := . )mapfMap[A, B] × A × B → Map[A, B]
. * .map-sepf(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. + .nat-basicfNat × Nat → Nat
. ++ .set-basicfSet[A] × A → Set[A]
. +1nat-basicfNat → Nat
. - .natpfNat × Nat → Nat with λ n, m. n ≥ m
. -* .map-sepf(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. -- .mapfMap[A, B] × A → Map[A, B]
. -- .set-unionfSet[A] × A → Set[A]
. -> .map-sepf(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. -⊗ .map-sepf(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. -1nat-basicpfNat → Nat with λ n. n ≠ 0
. < .nat-basicpNat × Nat
. => .refmap-mapletfRef[A] × A → Map[Ref[A], A] → Bool
. =>?refmap-ex-mapletfRef[A] → Map[Ref[A], A] → Bool
. =>_refmap-ex-mapletfRef[A] → Map[Ref[A], A] → Bool
. > .natpNat × Nat
. \ .set-unionfSet[A] × Set[A] → Set[A]
. \ .heapfuns-mapfMap[A, B] × Set[A] → Map[A, B]
. \ .heapfuns-mapfMap[A, B] × Map[A, B] → Map[A, B]
. ∈ .mapp'A × Map('A, 'B)
. ∈ .set-basicp'A × Set('A)
. ∩ .set-unionfSet[A] × Set[A] → Set[A]
. ∪ .set-unionfSet[A] × Set[A] → Set[A]
. ∪ .heapfuns-mapfMap[A, B] × Map[A, B] → Map[A, B]
. ≡ .refmap-separationpMap(Ref('A), 'A) × Map(Ref('A), 'A)
. ≤ .natpNat × Nat
. ≥ .natpNat × Nat
. ⊆ .mappMap('A, 'B) × Map('A, 'B)
. ⊆ .set-basicpSet('A) × Set('A)
. ⊆ .map-sepp(Map('A, 'B) → Bool) × (Map('A, 'B) → Bool)
. ⊗ .map-sepf(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. ⊥ .heapfuns-mappMap('A, 'B) × Map('A, 'B)
. and .map-sepf(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. exists ( . )set-unionpSet('A) × ('A → Bool)
. filter ( . )set-unionfSet[A] × (A → Bool) → Set[A]
. forall ( . )set-unionpSet('A) × ('A → Bool)
. leftnodefNode[A] → Ref[Node[A]]
. lefttreepfTree[A] → Tree[A] with λ t. t ≠ leaf
. left:= .nodefNode[A] × Ref[Node[A]] → Node[A]
. left:= .treepfTree[A] × Tree[A] → Tree[A] with λ t, t0. t ≠ leaf
. map ( . )set-unionfSet[A] × (A → B) → Set[B]
. or .map-sepf(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. rightnodefNode[A] → Ref[Node[A]]
. righttreepfTree[A] → Tree[A] with λ t. t ≠ leaf
. right:= .nodefNode[A] × Ref[Node[A]] → Node[A]
. right:= .treepfTree[A] × Tree[A] → Tree[A] with λ t, t0. t ≠ leaf
. valnodefNode[A] → A
. valtreepfTree[A] → A with λ t. t ≠ leaf
. val:= .nodefNode[A] × A → Node[A]
. val:= .treepfTree[A] × A → Tree[A] with λ t, val. t ≠ leaf
_∃ .refmap-mapletf(B → Map[Ref[A], A] → Bool) → Map[Ref[A], A] → Bool
_∃ .refmap-mapletf(B × C → Map[Ref[A], A] → Bool) → Map[Ref[A], A] → Bool
{ . }set-unionfA → Set[A]
{ . }map-sepfMap[A, B] → Map[A, B] → Bool
∅mapcMap[A, B]
∅set-basiccSet[A]
⌜ . ⌝map-sepfBool → Map[A, B] → Bool
Mapmaps
Natnat-basics
Nodenodes
Refpolyrefs
Setset-basics
Treetrees
Truerefmap-separationpBool
alinked-maptreevA
branchtreefTree[A] × A × Tree[A] → Tree[A]
disjointset-unionpSet('A) × Set('A)
dom .heapfuns-mapfMap[A, B] → Set[A]
empmap-seppMap('A, 'B)
falsemap-seppMap('A, 'B)
hlinked-maptreevMap[Ref[Node[A]], Node[A]]
hPlinked-maptreevMap[Ref[Node[A]], Node[A]] → Bool
itemap-sepfBool × (Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
leaftreecTree[A]
mknodenodefRef[Node[A]] × A × Ref[Node[A]] → Node[A]
not .map-sepf(Map[A, B] → Bool) → Map[A, B] → Bool
nullpolyrefcRef[A]
precisemap-sepp(Map('A, 'B) → Bool)
rlinked-maptreevRef[Node[A]]
tlinked-maptreevTree[A]
trlinked-maptreefRef[Node[A]] × Tree[A] → Map[Ref[Node[A]], Node[A]] → Bool
truemap-seppMap('A, 'B)