Mathbox for Mario Carneiro |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > df-fmla | Structured version Visualization version GIF version |
Description: Define the predicate which defines the set of valid Godel formulas. The parameter 𝑛 defines the maximum height of the formulas: the set (Fmla‘∅) is all formulas of the form 𝑥 = 𝑦 or 𝑥 ∈ 𝑦 (which in our coding scheme is the set ({∅, 1𝑜} × (ω × ω)); see df-sat 31325 for the full coding scheme), and each extra level adds to the complexity of the formulas in (Fmla‘𝑛). (Fmla‘ω) = ∪ 𝑛 ∈ ω(Fmla‘𝑛) is the set of all valid formulas. (Contributed by Mario Carneiro, 14-Jul-2013.) |
Ref | Expression |
---|---|
df-fmla | ⊢ Fmla = (𝑛 ∈ suc ω ↦ dom ((∅ Sat ∅)‘𝑛)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cfmla 31319 | . 2 class Fmla | |
2 | vn | . . 3 setvar 𝑛 | |
3 | com 7065 | . . . 4 class ω | |
4 | 3 | csuc 5725 | . . 3 class suc ω |
5 | 2 | cv 1482 | . . . . 5 class 𝑛 |
6 | c0 3915 | . . . . . 6 class ∅ | |
7 | csat 31318 | . . . . . 6 class Sat | |
8 | 6, 6, 7 | co 6650 | . . . . 5 class (∅ Sat ∅) |
9 | 5, 8 | cfv 5888 | . . . 4 class ((∅ Sat ∅)‘𝑛) |
10 | 9 | cdm 5114 | . . 3 class dom ((∅ Sat ∅)‘𝑛) |
11 | 2, 4, 10 | cmpt 4729 | . 2 class (𝑛 ∈ suc ω ↦ dom ((∅ Sat ∅)‘𝑛)) |
12 | 1, 11 | wceq 1483 | 1 wff Fmla = (𝑛 ∈ suc ω ↦ dom ((∅ Sat ∅)‘𝑛)) |
Colors of variables: wff setvar class |
This definition is referenced by: (None) |
Copyright terms: Public domain | W3C validator |