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Expression of type Conditional

from the theory of proveit.numbers.modular

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, a, b, c
from proveit.logic import And, Equals, InSet
from proveit.numbers import ModAbs, Mult, Real
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(Mult(a, ModAbs(b, c)), ModAbs(Mult(a, b), Mult(a, c))), And(InSet(a, Real), InSet(b, Real), InSet(c, Real)))
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(a \cdot \left|b\right|_{\textup{mod}\thinspace c}\right) = \left|a \cdot b\right|_{\textup{mod}\thinspace a \cdot c} \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R} ,  c \in \mathbb{R}\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, 11
7Operationoperator: 25
operands: 12
8Operationoperator: 22
operands: 13
9Operationoperator: 16
operands: 14
10Operationoperator: 16
operands: 15
11Operationoperator: 16
operands: 17
12ExprTuple28, 18
13ExprTuple19, 20
14ExprTuple28, 21
15ExprTuple27, 21
16Literal
17ExprTuple29, 21
18Operationoperator: 22
operands: 23
19Operationoperator: 25
operands: 24
20Operationoperator: 25
operands: 26
21Literal
22Literal
23ExprTuple27, 29
24ExprTuple28, 27
25Literal
26ExprTuple28, 29
27Variable
28Variable
29Variable