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, Q, f, g
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, Implies

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, g, Q], Implies(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)).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, Q\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \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)\right] \Rightarrow  \\ \left(\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) \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	32, 33, 26
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 23 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	12, 13
11	Lambda	parameters: 34 body: 14
12	Lambda	parameters: 25 body: 15
13	Lambda	parameters: 27 body: 16
14	Conditional	value: 17 condition: 18
15	Conditional	value: 19 condition: 20
16	Conditional	value: 21 condition: 22
17	Operation	operator: 23 operands: 24
18	Operation	operator: 26 operands: 34
19	Operation	operator: 32 operands: 25
20	Operation	operator: 26 operands: 25
21	Operation	operator: 33 operands: 27
22	Operation	operator: 26 operands: 27
23	Literal
24	ExprTuple	28, 29
25	ExprTuple	30
26	Variable
27	ExprTuple	31
28	Operation	operator: 32 operands: 34
29	Operation	operator: 33 operands: 34
30	ExprRange	lambda_map: 35 start_index: 41 end_index: 42
31	ExprRange	lambda_map: 36 start_index: 41 end_index: 42
32	Variable
33	Variable
34	ExprTuple	37
35	Lambda	parameter: 48 body: 38
36	Lambda	parameter: 48 body: 39
37	ExprRange	lambda_map: 40 start_index: 41 end_index: 42
38	IndexedVar	variable: 43 index: 48
39	IndexedVar	variable: 44 index: 48
40	Lambda	parameter: 48 body: 45
41	Literal
42	Variable
43	Variable
44	Variable
45	IndexedVar	variable: 46 index: 48
46	Variable
47	ExprTuple	48
48	Variable