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Expression of type Less

from the theory of proveit.numbers

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 a, b, c, d, x, y
from proveit.numbers import Add, Less, Mult
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Add(b, c)
sub_expr2 = Mult(Add(x, a), Add(c, y))
expr = Less(Add(Mult(Add(d, b), sub_expr1), sub_expr2), Add(Mult(Add(a, b), sub_expr1), sub_expr2))
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(d + b\right) \cdot \left(b + c\right)\right) + \left(\left(x + a\right) \cdot \left(c + y\right)\right)\right) < \left(\left(\left(a + b\right) \cdot \left(b + c\right)\right) + \left(\left(x + a\right) \cdot \left(c + y\right)\right)\right)
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, 4
3Operationoperator: 23
operands: 5
4Operationoperator: 23
operands: 6
5ExprTuple7, 9
6ExprTuple8, 9
7Operationoperator: 12
operands: 10
8Operationoperator: 12
operands: 11
9Operationoperator: 12
operands: 13
10ExprTuple14, 16
11ExprTuple15, 16
12Literal
13ExprTuple17, 18
14Operationoperator: 23
operands: 19
15Operationoperator: 23
operands: 20
16Operationoperator: 23
operands: 21
17Operationoperator: 23
operands: 22
18Operationoperator: 23
operands: 24
19ExprTuple25, 26
20ExprTuple28, 26
21ExprTuple26, 29
22ExprTuple27, 28
23Literal
24ExprTuple29, 30
25Variable
26Variable
27Variable
28Variable
29Variable
30Variable