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Proof step 7 from proof abs-log-toset-inter-restr-empty (previous step)

gstore[lnum] = groupblock(gndx, lax, m), abs-log(nx0, gstore).toSet ∩ (as | n) = ∅ ⊦ #((as | n) ∩ (lax.to-adr(lnum)).toSet) = 0, #(((lax.to-adr(lnum)).toSet ∪ abs-log(nx0, gstore).toSet) ∩ (as | n)) = 0, n = lnum, (as | n) ∩ (lax.to-adr(lnum)).toSet = ∅, n ∈ nx0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0)
Proof step 9:
gstore[lnum] = groupblock(gndx, lax, m), abs-log(nx0, gstore).toSet ∩ (as | n) = ∅ ⊦ #(((lax.to-adr(lnum)).toSet ∪ abs-log(nx0, gstore).toSet) ∩ (as | n)) = 0, #((as | n) ∩ (lax.to-adr(lnum)).toSet) = 0, n = lnum, n ∈ nx0, ∀ adr. adr ∈ (as | n) ∩ (lax.to-adr(lnum)).toSet ↔ adr ∈ ∅

Rule argument

spec: set-basic, inst: node-store name: Extension seq: ⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0) subst: [as0, as] → [∅, (as | n) ∩ (lax.to-adr(lnum)).toSet] flags: <all paths>

Additional information

Used terms: ∅, (as | n) ∩ (lax.to-adr(lnum)).toSet