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, ExprRange, IndexedVar, Lambda, Variable, a, n, x
from proveit.core_expr_types import a_1_to_n
from proveit.logic import And, Equals, InSet, Set
from proveit.numbers import Add, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_n], Conditional(Equals(Add(a_1_to_n), Mult(x, n)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Set(x)), one, 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(a_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \left\{\left(a_{1} +  a_{2} +  \ldots +  a_{n}\right) = \left(x \cdot n\right) \textrm{ if } \left(a_{1} \in \left\{x\right\}\right) \land  \left(a_{2} \in \left\{x\right\}\right) \land  \ldots \land  \left(a_{n} \in \left\{x\right\}\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: 12 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprRange	lambda_map: 15 start_index: 19 end_index: 20
11	Literal
12	ExprTuple	16
13	Literal
14	ExprTuple	30, 20
15	Lambda	parameter: 29 body: 17
16	ExprRange	lambda_map: 18 start_index: 19 end_index: 20
17	Operation	operator: 21 operands: 22
18	Lambda	parameter: 29 body: 23
19	Literal
20	Variable
21	Literal
22	ExprTuple	23, 24
23	IndexedVar	variable: 25 index: 29
24	Operation	operator: 27 operand: 30
25	Variable
26	ExprTuple	29
27	Literal
28	ExprTuple	30
29	Variable
30	Variable