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Expression of type ExprTuple

from the theory of proveit.numbers.exponentiation

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, ExprTuple, Lambda, a, x
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Exp, Log, RealPos, one
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, x], Conditional(Equals(Exp(a, Log(a, x)), x), And(InSet(a, RealPos), InSet(x, RealPos), NotEquals(a, one)))))
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(\left(a, x\right) \mapsto \left\{a^{\textrm{log}_a\left(x\right)} = x \textrm{ if } a \in \mathbb{R}^+ ,  x \in \mathbb{R}^+ ,  a \neq 1\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameters: 24
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 26
7Literal
8ExprTuple10, 11, 12
9Operationoperator: 13
operands: 14
10Operationoperator: 16
operands: 15
11Operationoperator: 16
operands: 17
12Operationoperator: 18
operands: 19
13Literal
14ExprTuple25, 20
15ExprTuple25, 21
16Literal
17ExprTuple26, 21
18Literal
19ExprTuple25, 22
20Operationoperator: 23
operands: 24
21Literal
22Literal
23Literal
24ExprTuple25, 26
25Variable
26Variable