Expression of type ExprTuple

from the theory of proveit.core_expr_types.lambda_maps

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 ExprTuple, Lambda
from proveit.core_expr_types import a_1_to_i, b_1_to_i, c_1_to_i, f__a_1_to_i, f__b_1_to_i, g__a_1_to_i, g__c_1_to_i
from proveit.logic import Equals, Forall

# build up the expression from sub-expressions
expr = ExprTuple(Forall(instance_param_or_params = [a_1_to_i], instance_expr = Equals(f__a_1_to_i, g__a_1_to_i)), Equals(Lambda([b_1_to_i], f__b_1_to_i), Lambda([c_1_to_i], g__c_1_to_i)).with_wrapping_at(2))

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(\forall_{a_{1}, a_{2}, \ldots, a_{i}}~\left(f\left(a_{1}, a_{2}, \ldots, a_{i}\right) = g\left(a_{1}, a_{2}, \ldots, a_{i}\right)\right), \begin{array}{c} \begin{array}{l} \left[\left(b_{1}, b_{2}, \ldots, b_{i}\right) \mapsto f\left(b_{1}, b_{2}, \ldots, b_{i}\right)\right] =  \\ \left[\left(c_{1}, c_{2}, \ldots, c_{i}\right) \mapsto g\left(c_{1}, c_{2}, \ldots, c_{i}\right)\right] \end{array} \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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