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Expression of type Conditional

from the theory of proveit.linear_algebra.scalar_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 import Conditional, K, alpha, beta, x
from proveit.linear_algebra import ScalarMult
from proveit.logic import And, Equals, InSet
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(ScalarMult(alpha, ScalarMult(beta, x)), ScalarMult(ScalarMult(alpha, beta), x)), And(InSet(alpha, K), InSet(beta, K)))
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\{\left(\alpha \cdot \left(\beta \cdot x\right)\right) = \left(\left(\alpha \cdot \beta\right) \cdot x\right) \textrm{ if } \alpha \in K ,  \beta \in K\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple9, 10
7Operationoperator: 20
operands: 11
8Operationoperator: 20
operands: 12
9Operationoperator: 14
operands: 13
10Operationoperator: 14
operands: 15
11ExprTuple23, 16
12ExprTuple17, 22
13ExprTuple23, 18
14Literal
15ExprTuple24, 18
16Operationoperator: 20
operands: 19
17Operationoperator: 20
operands: 21
18Variable
19ExprTuple24, 22
20Literal
21ExprTuple23, 24
22Variable
23Variable
24Variable