logo

Expression of type Implies

from the theory of proveit.linear_algebra.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 v, w, x, y, z
from proveit.linear_algebra import TensorProd, VecAdd
from proveit.logic import CartExp, Equals, Implies, InSet
from proveit.numbers import Real, three
In [2]:
# build up the expression from sub-expressions
sub_expr1 = TensorProd(y, z)
sub_expr2 = TensorProd(y, w)
sub_expr3 = TensorProd(y, v)
sub_expr4 = CartExp(Real, three)
sub_expr5 = TensorProd(x, VecAdd(sub_expr1, sub_expr2, sub_expr3))
expr = Implies(InSet(sub_expr5, TensorProd(sub_expr4, TensorProd(sub_expr4, sub_expr4))), Equals(VecAdd(TensorProd(x, sub_expr1), TensorProd(x, sub_expr2), TensorProd(x, sub_expr3)), sub_expr5).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(\left(x {\otimes} \left(\left(y {\otimes} z\right) + \left(y {\otimes} w\right) + \left(y {\otimes} v\right)\right)\right) \in \left(\mathbb{R}^{3} {\otimes} \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right)\right)\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(\left(x {\otimes} \left(y {\otimes} z\right)\right) + \left(x {\otimes} \left(y {\otimes} w\right)\right) + \left(x {\otimes} \left(y {\otimes} v\right)\right)\right) =  \\ \left(x {\otimes} \left(\left(y {\otimes} z\right) + \left(y {\otimes} w\right) + \left(y {\otimes} v\right)\right)\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: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple11, 9
7Literal
8ExprTuple10, 11
9Operationoperator: 35
operands: 12
10Operationoperator: 24
operands: 13
11Operationoperator: 35
operands: 14
12ExprTuple26, 15
13ExprTuple16, 17, 18
14ExprTuple27, 19
15Operationoperator: 35
operands: 20
16Operationoperator: 35
operands: 21
17Operationoperator: 35
operands: 22
18Operationoperator: 35
operands: 23
19Operationoperator: 24
operands: 25
20ExprTuple26, 26
21ExprTuple27, 28
22ExprTuple27, 29
23ExprTuple27, 30
24Literal
25ExprTuple28, 29, 30
26Operationoperator: 31
operands: 32
27Variable
28Operationoperator: 35
operands: 33
29Operationoperator: 35
operands: 34
30Operationoperator: 35
operands: 36
31Literal
32ExprTuple37, 38
33ExprTuple41, 39
34ExprTuple41, 40
35Literal
36ExprTuple41, 42
37Literal
38Literal
39Variable
40Variable
41Variable
42Variable