Description: A constructed two-slot structure. Version of 2strstr not depending on the hard-coded index value of the base set. (Contributed by AV, 22-Sep-2020) (Proof shortened by AV, 17-Oct-2024)
Ref | Expression | ||
---|---|---|---|
Hypotheses | 2str1.g | ⊢ 𝐺 = { 〈 ( Base ‘ ndx ) , 𝐵 〉 , 〈 𝑁 , + 〉 } | |
2str1.b | ⊢ ( Base ‘ ndx ) < 𝑁 | ||
2str1.n | ⊢ 𝑁 ∈ ℕ | ||
Assertion | 2strstr1 | ⊢ 𝐺 Struct 〈 ( Base ‘ ndx ) , 𝑁 〉 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2str1.g | ⊢ 𝐺 = { 〈 ( Base ‘ ndx ) , 𝐵 〉 , 〈 𝑁 , + 〉 } | |
2 | 2str1.b | ⊢ ( Base ‘ ndx ) < 𝑁 | |
3 | 2str1.n | ⊢ 𝑁 ∈ ℕ | |
4 | basendxnn | ⊢ ( Base ‘ ndx ) ∈ ℕ | |
5 | eqid | ⊢ ( Base ‘ ndx ) = ( Base ‘ ndx ) | |
6 | eqid | ⊢ 𝑁 = 𝑁 | |
7 | 4 5 2 3 6 | strle2 | ⊢ { 〈 ( Base ‘ ndx ) , 𝐵 〉 , 〈 𝑁 , + 〉 } Struct 〈 ( Base ‘ ndx ) , 𝑁 〉 |
8 | 1 7 | eqbrtri | ⊢ 𝐺 Struct 〈 ( Base ‘ ndx ) , 𝑁 〉 |