[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 19 from proof nodes-dealloc (previous step)

gstore[m] = groupblock(gndx, lax, m2), m ∈ gstore, @(m0, m1) ∈ lax ⊦ nodes(gstore -- n, ginval ++ n)[@(m, m0, m1)] = (nodes(gstore, ginval) \ (dom nodes(gstore, ginval) | n))[@(m, m0, m1)], m = n, m ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ ¬ adr ∈ as → (fs \ as)[adr] = fs[adr]
Proof step 21:
gstore[m] = groupblock(gndx, lax, m2), @(m0, m1) ∈ lax, m ∈ gstore ⊦ nodes(gstore -- n, ginval ++ n)[@(m, m0, m1)] = nodes(gstore, ginval)[@(m, m0, m1)], m = n, m ∈ ginval, @(m, m0, m1) ∈ dom nodes(gstore, ginval) | n

Rule argument

spec: store+set, inst: node-store name: Diff-get seq: ⊦ ¬ adr ∈ as → (fs \ as)[adr] = fs[adr] subst: [adr, as, fs] → [@(m, m0, m1), dom nodes(gstore, ginval) | n, nodes(gstore, ginval)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ adr ∈ as → (fs \ as)[adr] = (∅)[adr]; (s)% ⊦ adr ∈ as | n ↔ adr.lnum = n ∧ adr ∈ as; (ws)% ⊦ @(m, m0, m1).lnum = m; (s) Used terms: @(m, m0, m1), dom nodes(gstore, ginval) | n, nodes(gstore, ginval)