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 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 = 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(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]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	42, 43
2	Operation	operator: 16 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 46 body: 5
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15
12	Operation	operator: 16 operand: 21
13	Operation	operator: 32 operands: 18
14	Operation	operator: 34 operands: 19
15	Operation	operator: 34 operands: 20
16	Literal
17	ExprTuple	21
18	ExprTuple	22, 23
19	ExprTuple	49, 24
20	ExprTuple	50, 24
21	Lambda	parameter: 48 body: 25
22	ExprTuple	26
23	ExprTuple	27
24	Literal
25	Conditional	value: 28 condition: 29
26	ExprRange	lambda_map: 30 start_index: 49 end_index: 50
27	ExprRange	lambda_map: 31 start_index: 49 end_index: 50
28	Operation	operator: 32 operands: 33
29	Operation	operator: 34 operands: 35
30	Lambda	parameter: 47 body: 36
31	Lambda	parameter: 47 body: 37
32	Literal
33	ExprTuple	38, 39
34	Literal
35	ExprTuple	48, 40
36	Operation	operator: 42 operand: 47
37	Operation	operator: 43 operand: 47
38	Operation	operator: 42 operand: 48
39	Operation	operator: 43 operand: 48
40	Operation	operator: 45 operands: 46
41	ExprTuple	47
42	Variable
43	Variable
44	ExprTuple	48
45	Literal
46	ExprTuple	49, 50
47	Variable
48	Variable
49	Variable
50	Variable