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 ExprRange, Function, Lambda, P, Pk, Variable, i, j, k
from proveit.logic import Exists, Implies, Or
from proveit.numbers import Interval

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

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