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Expression of type Forall

from the theory of proveit.numbers.logarithms

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, Log, RealPos, greater, one
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, x, y], instance_expr = Less(Log(a, x), Log(a, y)), domain = RealPos, conditions = [Less(x, y), greater(a, one)])
Out[2]:
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, x, y \in \mathbb{R}^+~|~x < y, a > 1}~\left(\textrm{log}_a\left(x\right) < \textrm{log}_a\left(y\right)\right)
In [5]:
stored_expr.style_options()
Out[5]:
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()
Out[6]:
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple32, 29, 30
5Conditionalvalue: 6
condition: 7
6Operationoperator: 26
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 12
9Literal
10ExprTuple13, 14, 15, 16, 17
11Operationoperator: 19
operands: 18
12Operationoperator: 19
operands: 20
13Operationoperator: 23
operands: 21
14Operationoperator: 23
operands: 22
15Operationoperator: 23
operands: 24
16Operationoperator: 26
operands: 25
17Operationoperator: 26
operands: 27
18ExprTuple32, 29
19Literal
20ExprTuple32, 30
21ExprTuple32, 28
22ExprTuple29, 28
23Literal
24ExprTuple30, 28
25ExprTuple29, 30
26Literal
27ExprTuple31, 32
28Literal
29Variable
30Variable
31Literal
32Variable