lean4-htt/tests/lean/interactive/533.lean.expected.out
2022-08-04 20:55:13 -07:00

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{"textDocument": {"uri": "file://533.lean"},
"position": {"line": 2, "character": 10}}
{"items":
[{"label": "False",
"kind": 22,
"documentation":
{"value":
"`False` is the empty proposition. Thus, it has no introduction rules.\nIt represents a contradiction. `False` elimination rule, `False.rec`,\nexpresses the fact that anything follows from a contradiction.\nThis rule is sometimes called ex falso (short for ex falso sequitur quodlibet),\nor the principle of explosion.\nFor more information: [Propositional Logic](https://leanprover.github.io/theorem_proving_in_lean4/propositions_and_proofs.html#propositional-logic)\n",
"kind": "markdown"},
"detail": "Prop"},
{"label": "Fin",
"kind": 22,
"documentation":
{"value":
"`Fin n` is a natural number `i` with the constraint that `0 ≤ i < n`. ",
"kind": "markdown"},
"detail": "Nat → Type"},
{"label": "Float", "kind": 22, "detail": "Type"},
{"label": "FloatArray", "kind": 22, "detail": "Type"},
{"label": "FloatSpec", "kind": 22, "detail": "Type 1"},
{"label": "Foo", "kind": 6, "detail": "Sort ?u"},
{"label": "ForIn",
"kind": 7,
"detail":
"(Type u₁ → Type u₂) → Type u → outParam (Type v) → Type (max (max (max u (u₁ + 1)) u₂) v)"},
{"label": "ForIn'",
"kind": 7,
"detail":
"(Type u₁ → Type u₂) →\n (ρ : Type u) → (α : outParam (Type v)) → outParam (Membership α ρ) → Type (max (max (max u (u₁ + 1)) u₂) v)"},
{"label": "ForInStep",
"kind": 22,
"documentation":
{"value": "Auxiliary type used to compile `for x in xs` notation. ",
"kind": "markdown"},
"detail": "Type u → Type u"},
{"label": "ForM",
"kind": 7,
"documentation":
{"value":
"Typeclass for the polymorphic `forM` operation described in the \"do unchained\" paper.\nRemark:\n- `γ` is a \"container\" type of elements of type `α`.\n- `α` is treated as an output parameter by the typeclass resolution procedure.\n That is, it tries to find an instance using only `m` and `γ`.\n",
"kind": "markdown"},
"detail":
"(Type u → Type v) → Type w₁ → outParam (Type w₂) → Type (max (max (max (u + 1) v) w₁) w₂)"},
{"label": "Function", "kind": 9, "detail": "namespace"},
{"label": "Functor",
"kind": 7,
"detail": "(Type u → Type v) → Type (max (u + 1) v)"},
{"label": "failure",
"kind": 5,
"detail": "[self : Alternative f] → {α : Type u} → f α"},
{"label": "false", "kind": 4, "detail": "Bool"},
{"label": "false_and",
"kind": 3,
"detail": "∀ (p : Prop), (False ∧ p) = False"},
{"label": "false_iff", "kind": 3, "detail": "∀ (p : Prop), (False ↔ p) = ¬p"},
{"label": "false_implies",
"kind": 3,
"detail": "∀ (p : Prop), (False → p) = True"},
{"label": "false_of_ne", "kind": 3, "detail": "a ≠ a → False"},
{"label": "false_or", "kind": 3, "detail": "∀ (p : Prop), (False p) = p"},
{"label": "flip", "kind": 3, "detail": "(α → β → φ) → β → α → φ"},
{"label": "floatDecLe",
"kind": 3,
"detail": "(a b : Float) → Decidable (a ≤ b)"},
{"label": "floatDecLt",
"kind": 3,
"detail": "(a b : Float) → Decidable (a < b)"},
{"label": "floatSpec", "kind": 21, "detail": "FloatSpec"},
{"label": "forIn",
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"detail":
"[self : ForIn m ρ α] → {β : Type u₁} → [inst : Monad m] → ρ → β → (α → β → m (ForInStep β)) → m β"},
{"label": "forIn'",
"kind": 5,
"detail":
"[self : ForIn' m ρ α d] → {β : Type u₁} → [inst : Monad m] → (x : ρ) → β → ((a : α) → a ∈ x → β → m (ForInStep β)) → m β"},
{"label": "forM",
"kind": 5,
"detail":
"[self : ForM m γ α] → [inst : Monad m] → γ → (α → m PUnit) → m PUnit"},
{"label": "forall_congr",
"kind": 3,
"detail": "(∀ (a : α), p a = q a) → (∀ (a : α), p a) = ∀ (a : α), q a"},
{"label": "funext",
"kind": 3,
"detail": "(∀ (x : α), f₁ x = f₂ x) → f₁ = f₂"}],
"isIncomplete": true}