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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, g], Forall(instance_param_or_params = [i, j], instance_expr = 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])), domain = 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(f, g\right) \mapsto \left[\forall_{i, j \in \mathbb{Z}}~\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)\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	parameters: 2 body: 3
2	ExprTuple	43, 44
3	Operation	operator: 17 operand: 5
4	ExprTuple	5
5	Lambda	parameters: 47 body: 6
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operands: 10
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	15, 16
13	Operation	operator: 17 operand: 22
14	Operation	operator: 33 operands: 19
15	Operation	operator: 35 operands: 20
16	Operation	operator: 35 operands: 21
17	Literal
18	ExprTuple	22
19	ExprTuple	23, 24
20	ExprTuple	50, 25
21	ExprTuple	51, 25
22	Lambda	parameter: 49 body: 26
23	ExprTuple	27
24	ExprTuple	28
25	Literal
26	Conditional	value: 29 condition: 30
27	ExprRange	lambda_map: 31 start_index: 50 end_index: 51
28	ExprRange	lambda_map: 32 start_index: 50 end_index: 51
29	Operation	operator: 33 operands: 34
30	Operation	operator: 35 operands: 36
31	Lambda	parameter: 48 body: 37
32	Lambda	parameter: 48 body: 38
33	Literal
34	ExprTuple	39, 40
35	Literal
36	ExprTuple	49, 41
37	Operation	operator: 43 operand: 48
38	Operation	operator: 44 operand: 48
39	Operation	operator: 43 operand: 49
40	Operation	operator: 44 operand: 49
41	Operation	operator: 46 operands: 47
42	ExprTuple	48
43	Variable
44	Variable
45	ExprTuple	49
46	Literal
47	ExprTuple	50, 51
48	Variable
49	Variable
50	Variable
51	Variable