logo

Expression of type Conditional

from the theory of proveit.numbers.negation

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, ExprRange, IndexedVar, Variable, n, x
from proveit.core_expr_types import x_1_to_n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Complex, Neg, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(x, sub_expr1)
expr = Conditional(Equals(Neg(Add(x_1_to_n)), Add(ExprRange(sub_expr1, Neg(sub_expr2), one, n))), And(ExprRange(sub_expr1, InSet(sub_expr2, Complex), one, n)))
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\{\left(-\left(x_{1} +  x_{2} +  \ldots +  x_{n}\right)\right) = \left(- x_{1} -  x_{2} -  \ldots -  x_{n}\right) \textrm{ if } \left(x_{1} \in \mathbb{C}\right) \land  \left(x_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(x_{n} \in \mathbb{C}\right)\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
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple9
7Operationoperator: 27
operand: 13
8Operationoperator: 16
operands: 11
9ExprRangelambda_map: 12
start_index: 25
end_index: 26
10ExprTuple13
11ExprTuple14
12Lambdaparameter: 32
body: 15
13Operationoperator: 16
operands: 17
14ExprRangelambda_map: 18
start_index: 25
end_index: 26
15Operationoperator: 19
operands: 20
16Literal
17ExprTuple21
18Lambdaparameter: 32
body: 22
19Literal
20ExprTuple29, 23
21ExprRangelambda_map: 24
start_index: 25
end_index: 26
22Operationoperator: 27
operand: 29
23Literal
24Lambdaparameter: 32
body: 29
25Literal
26Variable
27Literal
28ExprTuple29
29IndexedVarvariable: 30
index: 32
30Variable
31ExprTuple32
32Variable