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, 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 = 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\{\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..

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	48, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	38, 39, 32
9	Operation	operator: 10 operands: 11
10	Literal
11	ExprTuple	12, 13
12	Operation	operator: 14 operand: 17
13	Operation	operator: 29 operands: 16
14	Literal
15	ExprTuple	17
16	ExprTuple	18, 19
17	Lambda	parameters: 40 body: 20
18	Lambda	parameters: 31 body: 21
19	Lambda	parameters: 33 body: 22
20	Conditional	value: 23 condition: 24
21	Conditional	value: 25 condition: 26
22	Conditional	value: 27 condition: 28
23	Operation	operator: 29 operands: 30
24	Operation	operator: 32 operands: 40
25	Operation	operator: 38 operands: 31
26	Operation	operator: 32 operands: 31
27	Operation	operator: 39 operands: 33
28	Operation	operator: 32 operands: 33
29	Literal
30	ExprTuple	34, 35
31	ExprTuple	36
32	Variable
33	ExprTuple	37
34	Operation	operator: 38 operands: 40
35	Operation	operator: 39 operands: 40
36	ExprRange	lambda_map: 41 start_index: 47 end_index: 48
37	ExprRange	lambda_map: 42 start_index: 47 end_index: 48
38	Variable
39	Variable
40	ExprTuple	43
41	Lambda	parameter: 54 body: 44
42	Lambda	parameter: 54 body: 45
43	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
44	IndexedVar	variable: 49 index: 54
45	IndexedVar	variable: 50 index: 54
46	Lambda	parameter: 54 body: 51
47	Literal
48	Variable
49	Variable
50	Variable
51	IndexedVar	variable: 52 index: 54
52	Variable
53	ExprTuple	54
54	Variable