Expression of type Lambda

from the theory of proveit.numbers.multiplication

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, Function, Lambda, Q, f
from proveit.core_expr_types import a_1_to_i, b_1_to_j, c_1_to_k
from proveit.numbers import Mult

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
expr = Lambda(sub_expr1, Conditional(Mult(a_1_to_i, Function(f, sub_expr1), c_1_to_k), Function(Q, sub_expr1)))

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(b_{1}, b_{2}, \ldots, b_{j}\right) \mapsto \left\{a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{i} \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{k} \textrm{ if } Q\left(b_{1}, b_{2}, \ldots, b_{j}\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: 13 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 13
4	Literal
5	ExprTuple	7, 8, 9
6	Variable
7	ExprRange	lambda_map: 10 start_index: 21 end_index: 11
8	Operation	operator: 12 operands: 13
9	ExprRange	lambda_map: 14 start_index: 21 end_index: 15
10	Lambda	parameter: 27 body: 16
11	Variable
12	Variable
13	ExprTuple	17
14	Lambda	parameter: 27 body: 18
15	Variable
16	IndexedVar	variable: 19 index: 27
17	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
18	IndexedVar	variable: 23 index: 27
19	Variable
20	Lambda	parameter: 27 body: 24
21	Literal
22	Variable
23	Variable
24	IndexedVar	variable: 25 index: 27
25	Variable
26	ExprTuple	27
27	Variable