Theorem struct2grstr

Description: A graph represented as an extensible structure with vertices as base set and indexed edges is actually an extensible structure. (Contributed by AV, 23-Nov-2020)

	Ref	Expression
Hypothesis	struct2grvtx.g	$$⊢G=\left\{⟨{\mathrm{Base}}_{\mathrm{ndx}},V⟩,⟨\mathrm{ef}\left(\mathrm{ndx}\right),E⟩\right\}$$
Assertion	struct2grstr	$$⊢G\mathrm{Struct}⟨{\mathrm{Base}}_{\mathrm{ndx}},\mathrm{ef}\left(\mathrm{ndx}\right)⟩$$

Proof

Step	Hyp	Ref	Expression
1		struct2grvtx.g	$$⊢G=\left\{⟨{\mathrm{Base}}_{\mathrm{ndx}},V⟩,⟨\mathrm{ef}\left(\mathrm{ndx}\right),E⟩\right\}$$
2		basendxltedgfndx	$$⊢{\mathrm{Base}}_{\mathrm{ndx}}<\mathrm{ef}\left(\mathrm{ndx}\right)$$
3		edgfndxnn	$$⊢\mathrm{ef}\left(\mathrm{ndx}\right)\in \mathbb{N}$$
4	1 2 3	2strstr1	$$⊢G\mathrm{Struct}⟨{\mathrm{Base}}_{\mathrm{ndx}},\mathrm{ef}\left(\mathrm{ndx}\right)⟩$$