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Expression of type Conditional

from the theory of proveit.numbers.absolute_value

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, ExprRange, IndexedVar, Variable, n, x
from proveit.core_expr_types import x_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import Abs, Add, Complex, LessEq, NaturalPos, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Forall(instance_param_or_params = [x_1_to_n], instance_expr = LessEq(Abs(Add(x_1_to_n)), Add(ExprRange(sub_expr1, Abs(IndexedVar(x, sub_expr1)), one, n))), domain = Complex), InSet(n, NaturalPos))
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\{\forall_{x_{1}, x_{2}, \ldots, x_{n} \in \mathbb{C}}~\left(\left|x_{1} +  x_{2} +  \ldots +  x_{n}\right| \leq \left(\left|x_{1}\right| +  \left|x_{2}\right| +  \ldots +  \left|x_{n}\right|\right)\right) \textrm{ if } n \in \mathbb{N}^+\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: 3
operand: 6
2Operationoperator: 27
operands: 5
3Literal
4ExprTuple6
5ExprTuple34, 7
6Lambdaparameters: 25
body: 8
7Literal
8Conditionalvalue: 9
condition: 10
9Operationoperator: 11
operands: 12
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple15, 16
13Literal
14ExprTuple17
15Operationoperator: 35
operand: 21
16Operationoperator: 24
operands: 19
17ExprRangelambda_map: 20
start_index: 33
end_index: 34
18ExprTuple21
19ExprTuple22
20Lambdaparameter: 40
body: 23
21Operationoperator: 24
operands: 25
22ExprRangelambda_map: 26
start_index: 33
end_index: 34
23Operationoperator: 27
operands: 28
24Literal
25ExprTuple29
26Lambdaparameter: 40
body: 30
27Literal
28ExprTuple37, 31
29ExprRangelambda_map: 32
start_index: 33
end_index: 34
30Operationoperator: 35
operand: 37
31Literal
32Lambdaparameter: 40
body: 37
33Literal
34Variable
35Literal
36ExprTuple37
37IndexedVarvariable: 38
index: 40
38Variable
39ExprTuple40
40Variable