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, i
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, InSet
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(i, Conditional(Forall(instance_param_or_params = [f, g, Q], instance_expr = 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)), 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_{f, g, Q}~\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) \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: 51 body: 3
2	ExprTuple	51
3	Conditional	value: 4 condition: 5
4	Operation	operator: 17 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	51, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	41, 42, 35
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 17 operand: 20
16	Operation	operator: 32 operands: 19
17	Literal
18	ExprTuple	20
19	ExprTuple	21, 22
20	Lambda	parameters: 43 body: 23
21	Lambda	parameters: 34 body: 24
22	Lambda	parameters: 36 body: 25
23	Conditional	value: 26 condition: 27
24	Conditional	value: 28 condition: 29
25	Conditional	value: 30 condition: 31
26	Operation	operator: 32 operands: 33
27	Operation	operator: 35 operands: 43
28	Operation	operator: 41 operands: 34
29	Operation	operator: 35 operands: 34
30	Operation	operator: 42 operands: 36
31	Operation	operator: 35 operands: 36
32	Literal
33	ExprTuple	37, 38
34	ExprTuple	39
35	Variable
36	ExprTuple	40
37	Operation	operator: 41 operands: 43
38	Operation	operator: 42 operands: 43
39	ExprRange	lambda_map: 44 start_index: 50 end_index: 51
40	ExprRange	lambda_map: 45 start_index: 50 end_index: 51
41	Variable
42	Variable
43	ExprTuple	46
44	Lambda	parameter: 57 body: 47
45	Lambda	parameter: 57 body: 48
46	ExprRange	lambda_map: 49 start_index: 50 end_index: 51
47	IndexedVar	variable: 52 index: 57
48	IndexedVar	variable: 53 index: 57
49	Lambda	parameter: 57 body: 54
50	Literal
51	Variable
52	Variable
53	Variable
54	IndexedVar	variable: 55 index: 57
55	Variable
56	ExprTuple	57
57	Variable