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, Forall, InSet
from proveit.numbers import Add, Integer, LessEq, one

# build up the expression from sub-expressions
expr = Lambda([i, j], Conditional(Forall(instance_param_or_params = [A], instance_expr = And(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), A, i, j)), conditions = [A, LessEq(i, Add(j, one))]), And(InSet(i, Integer), InSet(j, Integer))))

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\{\forall_{A~|~A, i \leq \left(j + 1\right)}~\left(A \land  A \land  ..\left(j - i - 2\right) \times.. \land  A\right) \textrm{ if } i \in \mathbb{Z} ,  j \in \mathbb{Z}\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	29, 34
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 20 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameter: 28 body: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	ExprTuple	28
12	Conditional	value: 16 condition: 17
13	ExprTuple	29, 18
14	Literal
15	ExprTuple	34, 18
16	Operation	operator: 20 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	28, 23
22	ExprRange	lambda_map: 24 start_index: 29 end_index: 34
23	Operation	operator: 25 operands: 26
24	Lambda	parameter: 31 body: 28
25	Literal
26	ExprTuple	29, 30
27	ExprTuple	31
28	Variable
29	Variable
30	Operation	operator: 32 operands: 33
31	Variable
32	Literal
33	ExprTuple	34, 35
34	Variable
35	Literal