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Expression of type Conditional

from the theory of proveit.numbers.addition

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, b
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.logic import InSet
from proveit.numbers import Add, Real, greater_eq
In [2]:
# build up the expression from sub-expressions
expr = Conditional(greater_eq(Add(a_1_to_i, b, c_1_to_j), b), InSet(b, Real))
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(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) \geq b \textrm{ if } b \in \mathbb{R}\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
4ExprTuple12, 7
5Literal
6ExprTuple12, 8
7Operationoperator: 9
operands: 10
8Literal
9Literal
10ExprTuple11, 12, 13
11ExprRangelambda_map: 14
start_index: 17
end_index: 15
12Variable
13ExprRangelambda_map: 16
start_index: 17
end_index: 18
14Lambdaparameter: 24
body: 19
15Variable
16Lambdaparameter: 24
body: 20
17Literal
18Variable
19IndexedVarvariable: 21
index: 24
20IndexedVarvariable: 22
index: 24
21Variable
22Variable
23ExprTuple24
24Variable