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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, x, y, z
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Complex, ComplexNonZero, Mult, frac
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [y], instance_expr = Equals(frac(Mult(x, y), Mult(x, z)), frac(y, z)), domain = Complex), And(InSet(x, ComplexNonZero), InSet(z, ComplexNonZero)))
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\{\forall_{y \in \mathbb{C}}~\left(\frac{x \cdot y}{x \cdot z} = \frac{y}{z}\right) \textrm{ if } x \in \mathbb{C}^{\neq 0} ,  z \in \mathbb{C}^{\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: 3
operand: 7
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7
5Literal
6ExprTuple8, 9
7Lambdaparameter: 32
body: 11
8Operationoperator: 19
operands: 12
9Operationoperator: 19
operands: 13
10ExprTuple32
11Conditionalvalue: 14
condition: 15
12ExprTuple33, 16
13ExprTuple34, 16
14Operationoperator: 17
operands: 18
15Operationoperator: 19
operands: 20
16Literal
17Literal
18ExprTuple21, 22
19Literal
20ExprTuple32, 23
21Operationoperator: 25
operands: 24
22Operationoperator: 25
operands: 26
23Literal
24ExprTuple27, 28
25Literal
26ExprTuple32, 34
27Operationoperator: 30
operands: 29
28Operationoperator: 30
operands: 31
29ExprTuple33, 32
30Literal
31ExprTuple33, 34
32Variable
33Variable
34Variable