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Expression of type Equals

from the theory of proveit.numbers.multiplication

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.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.logic import Equals
from proveit.numbers import Mult
In [2]:
# build up the expression from sub-expressions
expr = Equals(Mult(a_1_to_i, b_1_to_j, c_1_to_k), Mult(a_1_to_i, Mult(b_1_to_j), c_1_to_k)).with_wrapping_at(2)
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_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i}\cdot b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\right) =  \\ \left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot \left(b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k}\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.()(2)('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: 12
operands: 5
4Operationoperator: 12
operands: 6
5ExprTuple7, 17, 9
6ExprTuple7, 8, 9
7ExprRangelambda_map: 10
start_index: 21
end_index: 11
8Operationoperator: 12
operands: 13
9ExprRangelambda_map: 14
start_index: 21
end_index: 15
10Lambdaparameter: 27
body: 16
11Variable
12Literal
13ExprTuple17
14Lambdaparameter: 27
body: 18
15Variable
16IndexedVarvariable: 19
index: 27
17ExprRangelambda_map: 20
start_index: 21
end_index: 22
18IndexedVarvariable: 23
index: 27
19Variable
20Lambdaparameter: 27
body: 24
21Literal
22Variable
23Variable
24IndexedVarvariable: 25
index: 27
25Variable
26ExprTuple27
27Variable