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Expression of type Conditional

from the theory of proveit.numbers.division

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, x, y
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Integer, frac, zero
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(frac(x, a), frac(y, a)), And(InSet(a, Integer), InSet(x, Integer), InSet(y, Integer), Equals(x, y), NotEquals(a, zero)))
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\{\frac{x}{a} = \frac{y}{a} \textrm{ if } a \in \mathbb{Z} ,  x \in \mathbb{Z} ,  y \in \mathbb{Z} ,  x = y ,  a \neq 0\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: 20
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7
4Literal
5ExprTuple8, 9, 10, 11, 12
6Operationoperator: 14
operands: 13
7Operationoperator: 14
operands: 15
8Operationoperator: 18
operands: 16
9Operationoperator: 18
operands: 17
10Operationoperator: 18
operands: 19
11Operationoperator: 20
operands: 21
12Operationoperator: 22
operands: 23
13ExprTuple25, 27
14Literal
15ExprTuple26, 27
16ExprTuple27, 24
17ExprTuple25, 24
18Literal
19ExprTuple26, 24
20Literal
21ExprTuple25, 26
22Literal
23ExprTuple27, 28
24Literal
25Variable
26Variable
27Variable
28Literal