Expression of type Lambda

from the theory of proveit.core_expr_types.tuples

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, i, j, x
from proveit.core_expr_types import Len, f_i_to_j, range_i_to_jp1
from proveit.logic import Equals, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda([i, j], Conditional(Equals(Len(operands = [f_i_to_j, x]), Len(operands = [range_i_to_jp1])), InSet(Len(operands = [f_i_to_j]), 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(i, j\right) \mapsto \left\{|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right), x\right)| = |\left(i, \left(i + 1\right), \ldots, \left(j + 1\right)\right)| \textrm{ if } |\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right)| \in \mathbb{N}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	23, 27
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 15 operands: 13
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	Literal
13	ExprTuple	19, 17
14	ExprTuple	18
15	Literal
16	ExprTuple	19
17	Variable
18	ExprRange	lambda_map: 20 start_index: 23 end_index: 21
19	ExprRange	lambda_map: 22 start_index: 23 end_index: 27
20	Lambda	parameter: 31 body: 31
21	Operation	operator: 24 operands: 25
22	Lambda	parameter: 31 body: 26
23	Variable
24	Literal
25	ExprTuple	27, 28
26	Operation	operator: 29 operand: 31
27	Variable
28	Literal
29	Variable
30	ExprTuple	31
31	Variable