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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 π defines the maximum height of the formulas: the set (Fmlaββ ) is all formulas of the form π₯ β π¦ (which in our coding scheme is the set ({β } Γ (Ο Γ Ο)); see df-sat 34329 for the full coding scheme), see fmla0 34368, and each extra level adds to the complexity of the formulas in (Fmlaβπ), see fmlasuc 34372. Remark: it is sufficient to have atomic formulas of the form π₯ β π¦ only, because equations (formulas of the form π₯ = π¦), which are required as (atomic) formulas, can be introduced as a defined notion in terms of βπ, see df-goeq 34430. (FmlaβΟ) = βͺ π β Ο(Fmlaβπ) is the set of all valid formulas, see fmla 34367. (Contributed by Mario Carneiro, 14-Jul-2013.) |
Ref | Expression |
---|---|
df-fmla | β’ Fmla = (π β suc Ο β¦ dom ((β Sat β )βπ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cfmla 34323 | . 2 class Fmla | |
2 | vn | . . 3 setvar π | |
3 | com 7854 | . . . 4 class Ο | |
4 | 3 | csuc 6366 | . . 3 class suc Ο |
5 | 2 | cv 1540 | . . . . 5 class π |
6 | c0 4322 | . . . . . 6 class β | |
7 | csat 34322 | . . . . . 6 class Sat | |
8 | 6, 6, 7 | co 7408 | . . . . 5 class (β Sat β ) |
9 | 5, 8 | cfv 6543 | . . . 4 class ((β Sat β )βπ) |
10 | 9 | cdm 5676 | . . 3 class dom ((β Sat β )βπ) |
11 | 2, 4, 10 | cmpt 5231 | . 2 class (π β suc Ο β¦ dom ((β Sat β )βπ)) |
12 | 1, 11 | wceq 1541 | 1 wff Fmla = (π β suc Ο β¦ dom ((β Sat β )βπ)) |
Colors of variables: wff setvar class |
This definition is referenced by: fmlafv 34366 fmla 34367 fmlasuc0 34370 |
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