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Expression of type ExprTuple

from the theory of proveit.logic.sets.cardinality

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, N, S, Variable, n, x
from proveit.core_expr_types import Len, x_1_to_n
from proveit.logic import Equals, InSet
from proveit.numbers import 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(x, sub_expr1), S), one, n), Equals(Len(operands = [x_1_to_n]), N))
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(x_{1} \in S\right), \left(x_{2} \in S\right), \ldots, \left(x_{n} \in S\right), |\left(x_{1}, x_{2}, \ldots, x_{n}\right)| = N\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
1ExprRangelambda_map: 3
start_index: 16
end_index: 17
2Operationoperator: 4
operands: 5
3Lambdaparameter: 21
body: 6
4Literal
5ExprTuple7, 8
6Operationoperator: 9
operands: 10
7Operationoperator: 11
operands: 12
8Variable
9Literal
10ExprTuple18, 13
11Literal
12ExprTuple14
13Variable
14ExprRangelambda_map: 15
start_index: 16
end_index: 17
15Lambdaparameter: 21
body: 18
16Literal
17Variable
18IndexedVarvariable: 19
index: 21
19Variable
20ExprTuple21
21Variable