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Expression of type Conditional

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 Conditional, a, b
from proveit.logic import And, InSet
from proveit.numbers import Less, LessEq, Log, RealPos, greater_eq, one
In [2]:
# build up the expression from sub-expressions
expr = Conditional(greater_eq(Log(a, b), one), And(InSet(a, RealPos), InSet(b, RealPos), And(Less(one, a), LessEq(a, b)).with_total_ordering_style()))
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\{\textrm{log}_a\left(b\right) \geq 1 \textrm{ if } a \in \mathbb{R}^+ ,  b \in \mathbb{R}^+ ,  1 < a \leq b\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: 13
operands: 4
3ExprTuple22, 5
4ExprTuple6, 7, 8
5Operationoperator: 9
operands: 21
6Operationoperator: 11
operands: 10
7Operationoperator: 11
operands: 12
8Operationoperator: 13
operands: 14
9Literal
10ExprTuple23, 15
11Literal
12ExprTuple24, 15
13Literal
14ExprTuple16, 17
15Literal
16Operationoperator: 18
operands: 19
17Operationoperator: 20
operands: 21
18Literal
19ExprTuple22, 23
20Literal
21ExprTuple23, 24
22Literal
23Variable
24Variable