Expression of type ExprTuple

from the theory of proveit.core_expr_types.expr_arrays

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, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, VertExprArray, a, b, i
from proveit.core_expr_types import a_1_to_i, b_1_to_i
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import NaturalPos, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(i, Conditional(Forall(instance_param_or_params = [a_1_to_i, b_1_to_i], instance_expr = Equals(VertExprArray(a_1_to_i), VertExprArray(b_1_to_i)), condition = ExprRange(sub_expr1, Equals(IndexedVar(a, sub_expr1), IndexedVar(b, sub_expr1)), one, i)), InSet(i, NaturalPos))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(i \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b_{1}, b_{2}, \ldots, b_{i}~|~\left(a_{1} = b_{1}\right), \left(a_{2} = b_{2}\right), \ldots, \left(a_{i} = b_{i}\right)}~\left(\left(\begin{array}{cccc} 
 \multirow{1}{*}{$\begin{array}{c} \uparrow \\ a_{1} \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ a_{2} \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ \cdots \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ a_{i} \\ \downarrow \end{array}$} \\
\end{array}
\right) = \left(\begin{array}{cccc} 
 \multirow{1}{*}{$\begin{array}{c} \uparrow \\ b_{1} \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ b_{2} \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ \cdots \\ \downarrow \end{array}$} & \multirow{1}{*}{$\begin{array}{c} \uparrow \\ b_{i} \\ \downarrow \end{array}$} \\
\end{array}
\right)\right) \textrm{ if } i \in \mathbb{N}^+\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 28 body: 3
2	ExprTuple	28
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	28, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	22, 23
13	Conditional	value: 14 condition: 15
14	Operation	operator: 30 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21
19	ExprTuple	22
20	ExprTuple	23
21	ExprRange	lambda_map: 24 start_index: 27 end_index: 28
22	ExprRange	lambda_map: 25 start_index: 27 end_index: 28
23	ExprRange	lambda_map: 26 start_index: 27 end_index: 28
24	Lambda	parameter: 37 body: 29
25	Lambda	parameter: 37 body: 32
26	Lambda	parameter: 37 body: 33
27	Literal
28	Variable
29	Operation	operator: 30 operands: 31
30	Literal
31	ExprTuple	32, 33
32	IndexedVar	variable: 34 index: 37
33	IndexedVar	variable: 35 index: 37
34	Variable
35	Variable
36	ExprTuple	37
37	Variable