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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 Forall, InSet
from proveit.numbers import LessEq, RealNonPos, RealPos, frac
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x, y], instance_expr = LessEq(frac(a, x), frac(a, y)), domain = RealPos, condition = LessEq(x, y)), InSet(a, RealNonPos))
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_{x, y \in \mathbb{R}^+~|~x \leq y}~\left(\frac{a}{x} \leq \frac{a}{y}\right) \textrm{ if } a \in \mathbb{R}^{\le 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: 6
2Operationoperator: 23
operands: 5
3Literal
4ExprTuple6
5ExprTuple27, 7
6Lambdaparameters: 26
body: 8
7Literal
8Conditionalvalue: 9
condition: 10
9Operationoperator: 25
operands: 11
10Operationoperator: 12
operands: 13
11ExprTuple14, 15
12Literal
13ExprTuple16, 17, 18
14Operationoperator: 20
operands: 19
15Operationoperator: 20
operands: 21
16Operationoperator: 23
operands: 22
17Operationoperator: 23
operands: 24
18Operationoperator: 25
operands: 26
19ExprTuple27, 29
20Literal
21ExprTuple27, 30
22ExprTuple29, 28
23Literal
24ExprTuple30, 28
25Literal
26ExprTuple29, 30
27Variable
28Literal
29Variable
30Variable