Expression of type Lambda

from the theory of proveit.logic.booleans.disjunction

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 Exists, Implies, Or
from proveit.numbers import Add, Interval, LessEq, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(P, Conditional(Implies(Exists(instance_param_or_params = [k], instance_expr = Pk, domain = Interval(i, j)), Or(ExprRange(sub_expr1, Function(P, [sub_expr1]), i, j))), 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())

P \mapsto \left\{\left[\exists_{k \in \{i~\ldotp \ldotp~j\}}~P\left(k\right)\right] \Rightarrow \left(P\left(i\right) \lor  P\left(i + 1\right) \lor  \ldots \lor  P\left(j\right)\right) \textrm{ if } 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: 29 body: 2
1	ExprTuple	29
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	36, 11
9	Operation	operator: 12 operand: 18
10	Operation	operator: 14 operands: 15
11	Operation	operator: 16 operands: 17
12	Literal
13	ExprTuple	18
14	Literal
15	ExprTuple	19
16	Literal
17	ExprTuple	37, 20
18	Lambda	parameter: 31 body: 21
19	ExprRange	lambda_map: 22 start_index: 36 end_index: 37
20	Literal
21	Conditional	value: 23 condition: 24
22	Lambda	parameter: 33 body: 25
23	Operation	operator: 29 operand: 31
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operand: 33
26	ExprTuple	31
27	Literal
28	ExprTuple	31, 32
29	Variable
30	ExprTuple	33
31	Variable
32	Operation	operator: 34 operands: 35
33	Variable
34	Literal
35	ExprTuple	36, 37
36	Variable
37	Variable