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Expression of type Lambda

from the theory of proveit.logic.sets.enumeration

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, n, x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import Forall, InSet, NotInSet, Set
from proveit.logic.sets import x_notequals_all_y
from proveit.numbers import Natural
In [2]:
# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [x, y_1_to_n], instance_expr = NotInSet(x, Set(y_1_to_n)), condition = x_notequals_all_y), InSet(n, Natural)))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
n \mapsto \left\{\forall_{x, y_{1}, y_{2}, \ldots, y_{n}~|~\left(x \neq y_{1}\right), \left(x \neq y_{2}\right), \ldots, \left(x \neq y_{n}\right)}~\left(x \notin \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\right) \textrm{ if } n \in \mathbb{N}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 28
body: 2
1ExprTuple28
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Literal
8ExprTuple28, 10
9Lambdaparameters: 11
body: 12
10Literal
11ExprTuple31, 24
12Conditionalvalue: 13
condition: 14
13Operationoperator: 15
operands: 16
14Operationoperator: 17
operands: 18
15Literal
16ExprTuple31, 19
17Literal
18ExprTuple20
19Operationoperator: 21
operands: 22
20ExprRangelambda_map: 23
start_index: 27
end_index: 28
21Literal
22ExprTuple24
23Lambdaparameter: 35
body: 25
24ExprRangelambda_map: 26
start_index: 27
end_index: 28
25Operationoperator: 29
operands: 30
26Lambdaparameter: 35
body: 32
27Literal
28Variable
29Literal
30ExprTuple31, 32
31Variable
32IndexedVarvariable: 33
index: 35
33Variable
34ExprTuple35
35Variable