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 Conditional, ExprTuple, Lambda
from proveit.core_expr_types import Q__a_1_to_i, Q__b_1_to_i, Q__c_1_to_i, 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), condition = Q__a_1_to_i), Equals(Lambda([b_1_to_i], Conditional(f__b_1_to_i, Q__b_1_to_i)), Lambda([c_1_to_i], Conditional(g__c_1_to_i, Q__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}~|~Q\left(a_{1}, a_{2}, \ldots, a_{i}\right)}~\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 \left\{f\left(b_{1}, b_{2}, \ldots, b_{i}\right) \textrm{ if } Q\left(b_{1}, b_{2}, \ldots, b_{i}\right)\right..\right] =  \\ \left[\left(c_{1}, c_{2}, \ldots, c_{i}\right) \mapsto \left\{g\left(c_{1}, c_{2}, \ldots, c_{i}\right) \textrm{ if } Q\left(c_{1}, c_{2}, \ldots, c_{i}\right)\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: 18 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 29 body: 9
7	Lambda	parameters: 20 body: 10
8	Lambda	parameters: 22 body: 11
9	Conditional	value: 12 condition: 13
10	Conditional	value: 14 condition: 15
11	Conditional	value: 16 condition: 17
12	Operation	operator: 18 operands: 19
13	Operation	operator: 21 operands: 29
14	Operation	operator: 27 operands: 20
15	Operation	operator: 21 operands: 20
16	Operation	operator: 28 operands: 22
17	Operation	operator: 21 operands: 22
18	Literal
19	ExprTuple	23, 24
20	ExprTuple	25
21	Variable
22	ExprTuple	26
23	Operation	operator: 27 operands: 29
24	Operation	operator: 28 operands: 29
25	ExprRange	lambda_map: 30 start_index: 36 end_index: 37
26	ExprRange	lambda_map: 31 start_index: 36 end_index: 37
27	Variable
28	Variable
29	ExprTuple	32
30	Lambda	parameter: 43 body: 33
31	Lambda	parameter: 43 body: 34
32	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
33	IndexedVar	variable: 38 index: 43
34	IndexedVar	variable: 39 index: 43
35	Lambda	parameter: 43 body: 40
36	Literal
37	Variable
38	Variable
39	Variable
40	IndexedVar	variable: 41 index: 43
41	Variable
42	ExprTuple	43
43	Variable