[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 14 from proof prepost-restore-log (previous step)

elems(nx0 + n ' + nx2) ∩ ginval = ∅, inv(gstore2 \ ginval), elems(nx0 + n ' + nx2) ⊆ dom gstore2 ⊦ n ∈ gstore2 ∧ ¬ n ∈ ginval

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ ns ⊆ ns0 ↔ (∀ n. n ∈ ns → n ∈ ns0)
Proof step 16:
elems(nx0 + n ' + nx2) ∩ ginval = ∅, inv(gstore2 \ ginval), ∀ n0. n0 ∈ elems(nx0 + n ' + nx2) → n0 ∈ dom gstore2 ⊦ n ∈ gstore2 ∧ ¬ n ∈ ginval

Rule argument

spec: set-basic, inst: nat-set name: Subset seq: ⊦ ns ⊆ ns0 ↔ (∀ n. n ∈ ns → n ∈ ns0) subst: [ns0, ns] → [dom gstore2, elems(nx0 + n ' + nx2)] flags: <all paths>

Additional information

Used terms: dom gstore2, elems(nx0 + n ' + nx2)