logo

Expression of type LessEq

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 b
from proveit.core_expr_types import a_1_to_i, c_1_to_j
from proveit.numbers import Add, LessEq
In [2]:
# build up the expression from sub-expressions
expr = LessEq(Add(a_1_to_i, b, c_1_to_j), b)
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(a_{1} +  a_{2} +  \ldots +  a_{i} + b+ c_{1} +  c_{2} +  \ldots +  c_{j}\right) \leq b
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 7
3Operationoperator: 4
operands: 5
4Literal
5ExprTuple6, 7, 8
6ExprRangelambda_map: 9
start_index: 12
end_index: 10
7Variable
8ExprRangelambda_map: 11
start_index: 12
end_index: 13
9Lambdaparameter: 19
body: 14
10Variable
11Lambdaparameter: 19
body: 15
12Literal
13Variable
14IndexedVarvariable: 16
index: 19
15IndexedVarvariable: 17
index: 19
16Variable
17Variable
18ExprTuple19
19Variable