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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, m, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Forall, InSet, Intersect, NotInSet
from proveit.logic.sets import x_notin_some_A
from proveit.numbers import NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [x, A_1_to_m], instance_expr = NotInSet(x, Intersect(A_1_to_m)), condition = x_notin_some_A), InSet(m, 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(m \mapsto \left\{\forall_{x, A_{1}, A_{2}, \ldots, A_{m}~|~\left(x \notin A_{1}\right) \lor  \left(x \notin A_{2}\right) \lor  \ldots \lor  \left(x \notin A_{m}\right)}~\left(x \notin \left(A_{1} \cap  A_{2} \cap  \ldots \cap  A_{m}\right)\right) \textrm{ if } m \in \mathbb{N}^+\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
1Lambdaparameter: 28
body: 3
2ExprTuple28
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 10
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10
8Literal
9ExprTuple28, 11
10Lambdaparameters: 12
body: 13
11Literal
12ExprTuple31, 24
13Conditionalvalue: 14
condition: 15
14Operationoperator: 29
operands: 16
15Operationoperator: 17
operands: 18
16ExprTuple31, 19
17Literal
18ExprTuple20
19Operationoperator: 21
operands: 22
20ExprRangelambda_map: 23
start_index: 27
end_index: 28
21Literal
22ExprTuple24
23Lambdaparameter: 35
body: 25
24ExprRangelambda_map: 26
start_index: 27
end_index: 28
25Operationoperator: 29
operands: 30
26Lambdaparameter: 35
body: 32
27Literal
28Variable
29Literal
30ExprTuple31, 32
31Variable
32IndexedVarvariable: 33
index: 35
33Variable
34ExprTuple35
35Variable