Expression of type Conditional

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, Lambda, f, g, i
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, InSet
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [f, g], 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)), 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)), 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\{\forall_{f, g}~\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) \textrm{ if } i \in \mathbb{N}^+\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 14 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	41, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	31, 32
9	Operation	operator: 10 operands: 11
10	Literal
11	ExprTuple	12, 13
12	Operation	operator: 14 operand: 17
13	Operation	operator: 23 operands: 16
14	Literal
15	ExprTuple	17
16	ExprTuple	18, 19
17	Lambda	parameters: 33 body: 20
18	Lambda	parameters: 25 body: 21
19	Lambda	parameters: 26 body: 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 31 operands: 25
22	Operation	operator: 32 operands: 26
23	Literal
24	ExprTuple	27, 28
25	ExprTuple	29
26	ExprTuple	30
27	Operation	operator: 31 operands: 33
28	Operation	operator: 32 operands: 33
29	ExprRange	lambda_map: 34 start_index: 40 end_index: 41
30	ExprRange	lambda_map: 35 start_index: 40 end_index: 41
31	Variable
32	Variable
33	ExprTuple	36
34	Lambda	parameter: 47 body: 37
35	Lambda	parameter: 47 body: 38
36	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
37	IndexedVar	variable: 42 index: 47
38	IndexedVar	variable: 43 index: 47
39	Lambda	parameter: 47 body: 44
40	Literal
41	Variable
42	Variable
43	Variable
44	IndexedVar	variable: 45 index: 47
45	Variable
46	ExprTuple	47
47	Variable