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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, b
from proveit.logic import And, InSet
from proveit.numbers import Abs, Exp, LessEq, Real, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Abs(a)
expr = ExprTuple(Lambda([a, b], Conditional(LessEq(Exp(sub_expr1, two), Exp(b, two)), And(InSet(a, Real), InSet(b, Real), LessEq(sub_expr1, b)))))
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, b\right) \mapsto \left\{\left|a\right|^{2} \leq b^{2} \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R} ,  \left|a\right| \leq b\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: 2
body: 3
2ExprTuple28, 25
3Conditionalvalue: 4
condition: 5
4Operationoperator: 20
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13
9Operationoperator: 15
operands: 14
10Operationoperator: 15
operands: 16
11Operationoperator: 18
operands: 17
12Operationoperator: 18
operands: 19
13Operationoperator: 20
operands: 21
14ExprTuple24, 22
15Literal
16ExprTuple25, 22
17ExprTuple28, 23
18Literal
19ExprTuple25, 23
20Literal
21ExprTuple24, 25
22Literal
23Literal
24Operationoperator: 26
operand: 28
25Variable
26Literal
27ExprTuple28
28Variable