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Expression of type Lambda

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, Lambda, 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 = Lambda([a, b], 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(a, b\right) \mapsto \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()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 22
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 21
operands: 4
3Operationoperator: 14
operands: 5
4ExprTuple23, 6
5ExprTuple7, 8, 9
6Operationoperator: 10
operands: 22
7Operationoperator: 12
operands: 11
8Operationoperator: 12
operands: 13
9Operationoperator: 14
operands: 15
10Literal
11ExprTuple24, 16
12Literal
13ExprTuple25, 16
14Literal
15ExprTuple17, 18
16Literal
17Operationoperator: 19
operands: 20
18Operationoperator: 21
operands: 22
19Literal
20ExprTuple23, 24
21Literal
22ExprTuple24, 25
23Literal
24Variable
25Variable