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Expression of type Equals

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 a, b, n
from proveit.core_expr_types import Len, a_1_to_n
from proveit.logic import Equals
from proveit.numbers import Add, two
In [2]:
# build up the expression from sub-expressions
expr = Equals(Len(operands = [a, b, a_1_to_n]), Add(two, n)).with_wrapping_at(1)
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())
\begin{array}{c} \begin{array}{l} |\left(a, b,a_{1}, a_{2}, \ldots, a_{n}\right)| \\  = \left(2 + n\right) \end{array} \end{array}
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.()(1)('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: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple16, 9, 10
7Literal
8ExprTuple11, 14
9Variable
10ExprRangelambda_map: 12
start_index: 13
end_index: 14
11Literal
12Lambdaparameter: 18
body: 15
13Literal
14Variable
15IndexedVarvariable: 16
index: 18
16Variable
17ExprTuple18
18Variable