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Expression of type Conditional

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, 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 = 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())
\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()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 7
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7
5Literal
6ExprTuple26, 8
7Lambdaparameters: 9
body: 10
8Literal
9ExprTuple29, 22
10Conditionalvalue: 11
condition: 12
11Operationoperator: 13
operands: 14
12Operationoperator: 15
operands: 16
13Literal
14ExprTuple29, 17
15Literal
16ExprTuple18
17Operationoperator: 19
operands: 20
18ExprRangelambda_map: 21
start_index: 25
end_index: 26
19Literal
20ExprTuple22
21Lambdaparameter: 33
body: 23
22ExprRangelambda_map: 24
start_index: 25
end_index: 26
23Operationoperator: 27
operands: 28
24Lambdaparameter: 33
body: 30
25Literal
26Variable
27Literal
28ExprTuple29, 30
29Variable
30IndexedVarvariable: 31
index: 33
31Variable
32ExprTuple33
33Variable