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, ExprRange, Function, Lambda, Variable, f, i, j, m, n
from proveit.logic import Equals
from proveit.numbers import Add, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([f, i, j, m, n], Conditional(Equals([ExprRange(sub_expr1, ExprRange(sub_expr2, Function(f, [sub_expr1, sub_expr2]), i, j), m, n)], []), Equals(Add(n, one), m)))

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, m, n\right) \mapsto \left\{\left(f\left(m, i\right), f\left(m, i + 1\right), \ldots, f\left(m, j\right), f\left(m + 1, i\right), f\left(m + 1, i + 1\right), \ldots, f\left(m + 1, j\right), \ldots\ldots, f\left(n, i\right), f\left(n, i + 1\right), \ldots, f\left(n, j\right)\right) = () \textrm{ if } \left(n + 1\right) = m\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	25, 21, 22, 15, 16
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	10, 15
8	ExprTuple	11
9	ExprTuple
10	Operation	operator: 12 operands: 13
11	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
12	Literal
13	ExprTuple	16, 17
14	Lambda	parameter: 27 body: 19
15	Variable
16	Variable
17	Literal
18	ExprTuple	27
19	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
20	Lambda	parameter: 28 body: 24
21	Variable
22	Variable
23	ExprTuple	28
24	Operation	operator: 25 operands: 26
25	Variable
26	ExprTuple	27, 28
27	Variable
28	Variable