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Expression of type Equals

from the theory of proveit.numbers.absolute_value

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 ExprRange, IndexedVar, Variable, n, x
from proveit.core_expr_types import x_1_to_n
from proveit.logic import Equals
from proveit.numbers import Abs, Mult, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Abs(Mult(x_1_to_n)), Mult(ExprRange(sub_expr1, Abs(IndexedVar(x, sub_expr1)), 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|x_{1} \cdot  x_{2} \cdot  \ldots \cdot  x_{n}\right| = \left(\left|x_{1}\right| \cdot  \left|x_{2}\right| \cdot  \ldots \cdot  \left|x_{n}\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: 17
operand: 7
4Operationoperator: 9
operands: 6
5ExprTuple7
6ExprTuple8
7Operationoperator: 9
operands: 10
8ExprRangelambda_map: 11
start_index: 15
end_index: 16
9Literal
10ExprTuple12
11Lambdaparameter: 22
body: 13
12ExprRangelambda_map: 14
start_index: 15
end_index: 16
13Operationoperator: 17
operand: 19
14Lambdaparameter: 22
body: 19
15Literal
16Variable
17Literal
18ExprTuple19
19IndexedVarvariable: 20
index: 22
20Variable
21ExprTuple22
22Variable