Expression of type Lambda

from the theory of proveit.logic.booleans.conjunction

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 A, Conditional, ExprRange, Lambda, Variable, i, j
from proveit.logic import And
from proveit.numbers import Add, LessEq, one

# build up the expression from sub-expressions
expr = Lambda(A, Conditional(And(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), A, i, j)), And(A, LessEq(i, 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())

A \mapsto \left\{A \land  A \land  ..\left(j - i - 2\right) \times.. \land  A \textrm{ if } A ,  i \leq \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	parameter: 14 body: 2
1	ExprTuple	14
2	Conditional	value: 3 condition: 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8
6	Literal
7	ExprTuple	14, 9
8	ExprRange	lambda_map: 10 start_index: 15 end_index: 20
9	Operation	operator: 11 operands: 12
10	Lambda	parameter: 17 body: 14
11	Literal
12	ExprTuple	15, 16
13	ExprTuple	17
14	Variable
15	Variable
16	Operation	operator: 18 operands: 19
17	Variable
18	Literal
19	ExprTuple	20, 21
20	Variable
21	Literal