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Expression of type ExprTuple

from the theory of proveit.logic.sets.intersection

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, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import InSet, Intersect
from proveit.logic.sets import x_in_every_A
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x, A_1_to_m], Conditional(InSet(x, Intersect(A_1_to_m)), x_in_every_A)))
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, A_{1}, A_{2}, \ldots, A_{m}\right) \mapsto \left\{x \in \left(A_{1} \cap  A_{2} \cap  \ldots \cap  A_{m}\right) \textrm{ if } \left(x \in A_{1}\right) \land  \left(x \in A_{2}\right) \land  \ldots \land  \left(x \in A_{m}\right)\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
2ExprTuple21, 14
3Conditionalvalue: 4
condition: 5
4Operationoperator: 19
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple21, 9
7Literal
8ExprTuple10
9Operationoperator: 11
operands: 12
10ExprRangelambda_map: 13
start_index: 17
end_index: 18
11Literal
12ExprTuple14
13Lambdaparameter: 25
body: 15
14ExprRangelambda_map: 16
start_index: 17
end_index: 18
15Operationoperator: 19
operands: 20
16Lambdaparameter: 25
body: 22
17Literal
18Variable
19Literal
20ExprTuple21, 22
21Variable
22IndexedVarvariable: 23
index: 25
23Variable
24ExprTuple25
25Variable