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Expression of type Implies

from the theory of proveit.linear_algebra.tensors

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 u, y, z
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals, Implies
In [2]:
# build up the expression from sub-expressions
expr = Implies(Equals(y, u).with_wrapping_at(2), Equals(TensorProd(z, y), TensorProd(z, u)).with_wrapping_at(2)).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(\begin{array}{c} \begin{array}{l} y =  \\ u \end{array} \end{array}\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(z {\otimes} y\right) =  \\ \left(z {\otimes} u\right) \end{array} \end{array}\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: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple13, 15
6Literal
7ExprTuple8, 9
8Operationoperator: 11
operands: 10
9Operationoperator: 11
operands: 12
10ExprTuple14, 13
11Literal
12ExprTuple14, 15
13Variable
14Variable
15Variable