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Proof step 7 from proof abs-log-new (previous step)

gstore[lnum] = groupblock(gndx, lax, m), ax.toSet ∩ abs-log(nx0, gstore).toSet = ∅, ginval ∩ elems nx0 = ∅, new(ax, nodes(gstore, ginval)), lnum ∈ gstore, elems nx0 ⊆ dom gstore ⊦ #(ax.toSet ∩ (lax.to-adr(lnum)).toSet) = 0, #(ax.toSet ∩ ((lax.to-adr(lnum)).toSet ∪ abs-log(nx0, gstore).toSet)) = 0, ax.toSet ∩ (lax.to-adr(lnum)).toSet = ∅, lnum ∈ ginval

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), ginval ∩ elems nx0 = ∅, ax.toSet ∩ abs-log(nx0, gstore).toSet = ∅, new(ax, nodes(gstore, ginval)), lnum ∈ gstore, elems nx0 ⊆ dom gstore ⊦ #(ax.toSet ∩ ((lax.to-adr(lnum)).toSet ∪ abs-log(nx0, gstore).toSet)) = 0, #(ax.toSet ∩ (lax.to-adr(lnum)).toSet) = 0, lnum ∈ ginval, ∀ adr. adr ∈ ax.toSet ∩ (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] → [∅, ax.toSet ∩ (lax.to-adr(lnum)).toSet] flags: <all paths>

Additional information

Used terms: ∅, ax.toSet ∩ (lax.to-adr(lnum)).toSet