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, i, j, k
from proveit.core_expr_types import merge_back_equiv
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Natural, one, subtract

# build up the expression from sub-expressions
expr = Lambda([f, i, j, k], Conditional(merge_back_equiv, And(InSet(subtract(k, i), Natural), Equals(k, Add(j, 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, k\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right), f\left(k\right)\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(k\right)\right) \end{array} \end{array} \textrm{ if } \left(k - i\right) \in \mathbb{N} ,  k = \left(j + 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	28, 37, 32, 30
2	Conditional	value: 3 condition: 4
3	Operation	operator: 17 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	ExprTuple	12, 13
9	ExprTuple	14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 17 operands: 18
12	ExprRange	lambda_map: 20 start_index: 37 end_index: 32
13	Operation	operator: 28 operand: 30
14	ExprRange	lambda_map: 20 start_index: 37 end_index: 30
15	Literal
16	ExprTuple	21, 22
17	Literal
18	ExprTuple	30, 23
19	ExprTuple	30
20	Lambda	parameter: 34 body: 24
21	Operation	operator: 26 operands: 25
22	Literal
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operand: 34
25	ExprTuple	30, 31
26	Literal
27	ExprTuple	32, 33
28	Variable
29	ExprTuple	34
30	Variable
31	Operation	operator: 35 operand: 37
32	Variable
33	Literal
34	Variable
35	Literal
36	ExprTuple	37
37	Variable