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, f, g
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, Implies

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, g], Implies(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)).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(\left(f, g\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \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)\right] \Rightarrow  \\ \left(\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) \end{array} \end{array}\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	parameters: 2 body: 3
2	ExprTuple	25, 26
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 17 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	12, 13
11	Lambda	parameters: 27 body: 14
12	Lambda	parameters: 19 body: 15
13	Lambda	parameters: 20 body: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 25 operands: 19
16	Operation	operator: 26 operands: 20
17	Literal
18	ExprTuple	21, 22
19	ExprTuple	23
20	ExprTuple	24
21	Operation	operator: 25 operands: 27
22	Operation	operator: 26 operands: 27
23	ExprRange	lambda_map: 28 start_index: 34 end_index: 35
24	ExprRange	lambda_map: 29 start_index: 34 end_index: 35
25	Variable
26	Variable
27	ExprTuple	30
28	Lambda	parameter: 41 body: 31
29	Lambda	parameter: 41 body: 32
30	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
31	IndexedVar	variable: 36 index: 41
32	IndexedVar	variable: 37 index: 41
33	Lambda	parameter: 41 body: 38
34	Literal
35	Variable
36	Variable
37	Variable
38	IndexedVar	variable: 39 index: 41
39	Variable
40	ExprTuple	41
41	Variable