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, f, fi, fj, i, j
from proveit.core_expr_types import f_i_to_j
from proveit.logic import Equals
from proveit.numbers import Add, one

# build up the expression from sub-expressions
expr = Lambda([f, i, j], Conditional(Equals([fi, fj], [f_i_to_j]), Equals(j, Add(i, one))))

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