[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 5 from proof log-disjoint-istore (previous step)

elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, ∀ n. (n < # lpt ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size), ∀ n. (n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size) ⊦ #(dom istore ∩ elems nx) = 0, ∀ n. n ∈ dom istore ∩ elems nx ↔ n ∈ ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, n ∈ istore, n ∈ nx, n ∈ gstore, ∀ n. (n < # lpt ∧ lpt[n].flags = LP_GROUP_NODES ↔ n ∈ gstore) ∧ (n ∈ gstore ∧ ¬ n ∈ ginval → abs-leb(avol[n], gstore[n], lpt[n])) ∧ (n ∈ gstore → lpt[n].ref-size = gstore[n].ref-size), ∀ n. (n < # lpt ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size) ⊦ #(dom istore ∩ elems nx) = 0, n ∈ ginval

Rule argument

Additional information

Used simplifier rules: fwd-in-log-in-gstore: ⊦ n ∈ nx ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → n ∈ gstore; (forward) from specification apersistence-base%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]%elems-in-notin-ginval: ⊦ n ∈ nx ∧ elems nx ∩ ns = ∅ → ¬ n ∈ ns; (forward) from specification apersistence-base%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]% ⊦ n ∈ elems nx ↔ n ∈ nx; (s)% ⊦ n ∈ dom istore ↔ n ∈ istore; (s)% ⊦ n ∈ ns ∩ ns0 ↔ n ∈ ns ∧ n ∈ ns0; (ws)% ⊦ ¬ n ∈ ∅; (s)