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 Conditional, ExprRange, Function, Lambda, P, Pk, Variable, i, j, k
from proveit.logic import And, Forall, Implies, InSet
from proveit.numbers import Integer, Interval

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([i, j], Conditional(Forall(instance_param_or_params = [P], instance_expr = Implies(And(ExprRange(sub_expr1, Function(P, [sub_expr1]), i, j)), Forall(instance_param_or_params = [k], instance_expr = Pk, domain = Interval(i, j)))), 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_{P}~\left(\left(P\left(i\right) \land  P\left(i + 1\right) \land  \ldots \land  P\left(j\right)\right) \Rightarrow \left[\forall_{k \in \{i~\ldotp \ldotp~j\}}~P\left(k\right)\right]\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: 38 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 20 operand: 6
3	Operation	operator: 18 operands: 5
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 30 body: 10
7	Operation	operator: 32 operands: 11
8	Operation	operator: 32 operands: 12
9	ExprTuple	30
10	Operation	operator: 13 operands: 14
11	ExprTuple	39, 15
12	ExprTuple	40, 15
13	Literal
14	ExprTuple	16, 17
15	Literal
16	Operation	operator: 18 operands: 19
17	Operation	operator: 20 operand: 23
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	23
22	ExprRange	lambda_map: 24 start_index: 39 end_index: 40
23	Lambda	parameter: 35 body: 25
24	Lambda	parameter: 34 body: 26
25	Conditional	value: 27 condition: 28
26	Operation	operator: 30 operand: 34
27	Operation	operator: 30 operand: 35
28	Operation	operator: 32 operands: 33
29	ExprTuple	34
30	Variable
31	ExprTuple	35
32	Literal
33	ExprTuple	35, 36
34	Variable
35	Variable
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Variable