Expression of type ExprTuple

from the theory of proveit.core_expr_types.tuples

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, ExprTuple, Lambda, i, j, k
from proveit.core_expr_types import f_i_to_j, fk, g_i_to_j, gk
from proveit.logic import And, Equals, Forall, Implies, InSet
from proveit.numbers import Integer, Interval

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j], Conditional(Implies(Forall(instance_param_or_params = [k], instance_expr = Equals(fk, gk), domain = Interval(i, j)), Equals([f_i_to_j], [g_i_to_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(\left(i, j\right) \mapsto \left\{\left[\forall_{k \in \{i~\ldotp \ldotp~j\}}~\left(f\left(k\right) = g\left(k\right)\right)\right] \Rightarrow \left(\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right) = \left(g\left(i\right), g\left(i + 1\right), \ldots, g\left(j\right)\right)\right) \textrm{ if } i \in \mathbb{Z} ,  j \in \mathbb{Z}\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	parameters: 43 body: 2
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	11, 12
9	Operation	operator: 13 operand: 18
10	Operation	operator: 29 operands: 15
11	Operation	operator: 31 operands: 16
12	Operation	operator: 31 operands: 17
13	Literal
14	ExprTuple	18
15	ExprTuple	19, 20
16	ExprTuple	46, 21
17	ExprTuple	47, 21
18	Lambda	parameter: 45 body: 22
19	ExprTuple	23
20	ExprTuple	24
21	Literal
22	Conditional	value: 25 condition: 26
23	ExprRange	lambda_map: 27 start_index: 46 end_index: 47
24	ExprRange	lambda_map: 28 start_index: 46 end_index: 47
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operands: 32
27	Lambda	parameter: 44 body: 33
28	Lambda	parameter: 44 body: 34
29	Literal
30	ExprTuple	35, 36
31	Literal
32	ExprTuple	45, 37
33	Operation	operator: 39 operand: 44
34	Operation	operator: 40 operand: 44
35	Operation	operator: 39 operand: 45
36	Operation	operator: 40 operand: 45
37	Operation	operator: 42 operands: 43
38	ExprTuple	44
39	Variable
40	Variable
41	ExprTuple	45
42	Literal
43	ExprTuple	46, 47
44	Variable
45	Variable
46	Variable
47	Variable