Expression of type Conditional

from the theory of proveit.logic.equality

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, P, n
from proveit.core_expr_types import P__x_1_to_n, P__y_1_to_n, x_1_to_n, x_eq_y__1_to_n, y_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [P, x_1_to_n, y_1_to_n], instance_expr = P__y_1_to_n, conditions = [P__x_1_to_n, x_eq_y__1_to_n]), InSet(n, Natural))

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_{P, x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}~|~P\left(x_{1}, x_{2}, \ldots, x_{n}\right),\left(x_{1} = y_{1}\right), \left(x_{2} = y_{2}\right), \ldots, \left(x_{n} = y_{n}\right)}~P\left(y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } n \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: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	27, 8
7	Lambda	parameters: 9 body: 10
8	Literal
9	ExprTuple	20, 23, 16
10	Conditional	value: 11 condition: 12
11	Operation	operator: 20 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16
14	Literal
15	ExprTuple	17, 18
16	ExprRange	lambda_map: 19 start_index: 26 end_index: 27
17	Operation	operator: 20 operands: 21
18	ExprRange	lambda_map: 22 start_index: 26 end_index: 27
19	Lambda	parameter: 35 body: 31
20	Variable
21	ExprTuple	23
22	Lambda	parameter: 35 body: 24
23	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
24	Operation	operator: 28 operands: 29
25	Lambda	parameter: 35 body: 30
26	Literal
27	Variable
28	Literal
29	ExprTuple	30, 31
30	IndexedVar	variable: 32 index: 35
31	IndexedVar	variable: 33 index: 35
32	Variable
33	Variable
34	ExprTuple	35
35	Variable