Expression of type Conditional

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, 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 = 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[\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 11 operand: 16
8	Operation	operator: 27 operands: 13
9	Operation	operator: 29 operands: 14
10	Operation	operator: 29 operands: 15
11	Literal
12	ExprTuple	16
13	ExprTuple	17, 18
14	ExprTuple	44, 19
15	ExprTuple	45, 19
16	Lambda	parameter: 43 body: 20
17	ExprTuple	21
18	ExprTuple	22
19	Literal
20	Conditional	value: 23 condition: 24
21	ExprRange	lambda_map: 25 start_index: 44 end_index: 45
22	ExprRange	lambda_map: 26 start_index: 44 end_index: 45
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operands: 30
25	Lambda	parameter: 42 body: 31
26	Lambda	parameter: 42 body: 32
27	Literal
28	ExprTuple	33, 34
29	Literal
30	ExprTuple	43, 35
31	Operation	operator: 37 operand: 42
32	Operation	operator: 38 operand: 42
33	Operation	operator: 37 operand: 43
34	Operation	operator: 38 operand: 43
35	Operation	operator: 40 operands: 41
36	ExprTuple	42
37	Variable
38	Variable
39	ExprTuple	43
40	Literal
41	ExprTuple	44, 45
42	Variable
43	Variable
44	Variable
45	Variable