Expression of type ExprTuple

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

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(P, Implies(And(ExprRange(sub_expr1, Function(P, [sub_expr1]), i, j)), Forall(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())

\left(P \mapsto \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)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 20 body: 3
2	ExprTuple	20
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operand: 13
8	Literal
9	ExprTuple	12
10	Literal
11	ExprTuple	13
12	ExprRange	lambda_map: 14 start_index: 29 end_index: 30
13	Lambda	parameter: 25 body: 15
14	Lambda	parameter: 24 body: 16
15	Conditional	value: 17 condition: 18
16	Operation	operator: 20 operand: 24
17	Operation	operator: 20 operand: 25
18	Operation	operator: 22 operands: 23
19	ExprTuple	24
20	Variable
21	ExprTuple	25
22	Literal
23	ExprTuple	25, 26
24	Variable
25	Variable
26	Operation	operator: 27 operands: 28
27	Literal
28	ExprTuple	29, 30
29	Variable
30	Variable