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Expression of type ExprTuple

from the theory of proveit.logic.equality

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, f, n
from proveit.core_expr_types import f__x_1_to_n, f__y_1_to_n, x_1_to_n, x_eq_y__1_to_n, y_1_to_n
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [f, x_1_to_n, y_1_to_n], instance_expr = Equals(f__x_1_to_n, f__y_1_to_n), condition = x_eq_y__1_to_n), 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(n \mapsto \left\{\forall_{f, x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}~|~\left(x_{1} = y_{1}\right), \left(x_{2} = y_{2}\right), \ldots, \left(x_{n} = y_{n}\right)}~\left(f\left(x_{1}, x_{2}, \ldots, x_{n}\right) = f\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right) \textrm{ if } n \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: 32
body: 3
2ExprTuple32
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 10
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10
8Literal
9ExprTuple32, 11
10Lambdaparameters: 12
body: 13
11Literal
12ExprTuple23, 26, 27
13Conditionalvalue: 14
condition: 15
14Operationoperator: 33
operands: 16
15Operationoperator: 17
operands: 18
16ExprTuple19, 20
17Literal
18ExprTuple21
19Operationoperator: 23
operands: 22
20Operationoperator: 23
operands: 24
21ExprRangelambda_map: 25
start_index: 31
end_index: 32
22ExprTuple26
23Variable
24ExprTuple27
25Lambdaparameter: 40
body: 28
26ExprRangelambda_map: 29
start_index: 31
end_index: 32
27ExprRangelambda_map: 30
start_index: 31
end_index: 32
28Operationoperator: 33
operands: 34
29Lambdaparameter: 40
body: 35
30Lambdaparameter: 40
body: 36
31Literal
32Variable
33Literal
34ExprTuple35, 36
35IndexedVarvariable: 37
index: 40
36IndexedVarvariable: 38
index: 40
37Variable
38Variable
39ExprTuple40
40Variable