Expression of type Lambda

from the theory of proveit.logic.sets

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, ExprRange, IndexedVar, Lambda, S, Variable, n, y
from proveit.core_expr_types import Q__y_1_to_n, f__y_1_to_n, y_1_to_n
from proveit.logic import And, InSet
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([y_1_to_n], Conditional(f__y_1_to_n, And(ExprRange(sub_expr1, InSet(IndexedVar(y, sub_expr1), IndexedVar(S, sub_expr1)), one, n), Q__y_1_to_n)))

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(y_{1}, y_{2}, \ldots, y_{n}\right) \mapsto \left\{f\left(y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } \left(y_{1} \in S_{1}\right) ,  \left(y_{2} \in S_{2}\right) ,  \ldots ,  \left(y_{n} \in S_{n}\right) ,  Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 11 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 11
3	Operation	operator: 5 operands: 6
4	Variable
5	Literal
6	ExprTuple	7, 8
7	ExprRange	lambda_map: 9 start_index: 17 end_index: 18
8	Operation	operator: 10 operands: 11
9	Lambda	parameter: 24 body: 12
10	Variable
11	ExprTuple	13
12	Operation	operator: 14 operands: 15
13	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
14	Literal
15	ExprTuple	20, 19
16	Lambda	parameter: 24 body: 20
17	Literal
18	Variable
19	IndexedVar	variable: 21 index: 24
20	IndexedVar	variable: 22 index: 24
21	Variable
22	Variable
23	ExprTuple	24
24	Variable