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Expression of type ExprTuple

from the theory of proveit.numbers.multiplication

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 ExprRange, ExprTuple, IndexedVar, Variable, a, b, i, j, x, y
from proveit.logic import InSet
from proveit.numbers import LessEq, RealNonNeg, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), RealNonNeg), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), RealNonNeg), one, j), LessEq(x, y))
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_{1} \in \mathbb{R}^{\ge 0}\right), \left(a_{2} \in \mathbb{R}^{\ge 0}\right), \ldots, \left(a_{i} \in \mathbb{R}^{\ge 0}\right),\left(b_{1} \in \mathbb{R}^{\ge 0}\right), \left(b_{2} \in \mathbb{R}^{\ge 0}\right), \ldots, \left(b_{j} \in \mathbb{R}^{\ge 0}\right), x \leq y\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1, 2, 3
1ExprRangelambda_map: 4
start_index: 7
end_index: 5
2ExprRangelambda_map: 6
start_index: 7
end_index: 8
3Operationoperator: 9
operands: 10
4Lambdaparameter: 24
body: 11
5Variable
6Lambdaparameter: 24
body: 12
7Literal
8Variable
9Literal
10ExprTuple13, 14
11Operationoperator: 16
operands: 15
12Operationoperator: 16
operands: 17
13Variable
14Variable
15ExprTuple18, 20
16Literal
17ExprTuple19, 20
18IndexedVarvariable: 21
index: 24
19IndexedVarvariable: 22
index: 24
20Literal
21Variable
22Variable
23ExprTuple24
24Variable