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Expression of type Forall

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 a, x, y
from proveit.logic import Forall
from proveit.numbers import Less, RealNeg, RealPos, frac, greater
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a], instance_expr = Forall(instance_param_or_params = [x, y], instance_expr = greater(frac(a, x), frac(a, y)), domain = RealNeg, condition = Less(x, y)), domain = RealPos)
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())
\forall_{a \in \mathbb{R}^+}~\left[\forall_{x, y \in \mathbb{R}^-~|~x < y}~\left(\frac{a}{x} > \frac{a}{y}\right)\right]
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 31
body: 4
3ExprTuple31
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 27
operands: 9
7Literal
8ExprTuple10
9ExprTuple31, 11
10Lambdaparameters: 30
body: 12
11Literal
12Conditionalvalue: 13
condition: 14
13Operationoperator: 29
operands: 15
14Operationoperator: 16
operands: 17
15ExprTuple18, 19
16Literal
17ExprTuple20, 21, 22
18Operationoperator: 24
operands: 23
19Operationoperator: 24
operands: 25
20Operationoperator: 27
operands: 26
21Operationoperator: 27
operands: 28
22Operationoperator: 29
operands: 30
23ExprTuple31, 34
24Literal
25ExprTuple31, 33
26ExprTuple33, 32
27Literal
28ExprTuple34, 32
29Literal
30ExprTuple33, 34
31Variable
32Literal
33Variable
34Variable