Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 42 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 12 operand: 17
9	Operation	operator: 28 operands: 14
10	Operation	operator: 30 operands: 15
11	Operation	operator: 30 operands: 16
12	Literal
13	ExprTuple	17
14	ExprTuple	18, 19
15	ExprTuple	45, 20
16	ExprTuple	46, 20
17	Lambda	parameter: 44 body: 21
18	ExprTuple	22
19	ExprTuple	23
20	Literal
21	Conditional	value: 24 condition: 25
22	ExprRange	lambda_map: 26 start_index: 45 end_index: 46
23	ExprRange	lambda_map: 27 start_index: 45 end_index: 46
24	Operation	operator: 28 operands: 29
25	Operation	operator: 30 operands: 31
26	Lambda	parameter: 43 body: 32
27	Lambda	parameter: 43 body: 33
28	Literal
29	ExprTuple	34, 35
30	Literal
31	ExprTuple	44, 36
32	Operation	operator: 38 operand: 43
33	Operation	operator: 39 operand: 43
34	Operation	operator: 38 operand: 44
35	Operation	operator: 39 operand: 44
36	Operation	operator: 41 operands: 42
37	ExprTuple	43
38	Variable
39	Variable
40	ExprTuple	44
41	Literal
42	ExprTuple	45, 46
43	Variable
44	Variable
45	Variable
46	Variable