[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 inv-allocate-ind (previous step)

remove-refsize0(gstore1) = gstore1, remove-refsize0(istore0) = istore0, elems nx ∩ ginval2 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval2, inv(gstore2 \ ginval2), inv(gstore1), inv(istore), inv(istore0), (dom istore).max + 1 ∈ istore, istore0 ⊑ istore, pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2, pstate.index? → pstate.lnum ∈ istore ⊦ dups(nx)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ istore ≠ ∅ ∧ n > (dom istore).max → (n ∈ istore ↔ false)

Rule argument

spec: nat-store+set, inst: index-store name: dom-max-in seq: ⊦ istore ≠ ∅ ∧ n > (dom istore).max → (n ∈ istore ↔ false) subst: [istore, n] → [istore, (dom istore).max + 1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m > n ↔ n < m; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ ¬ n < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ inv(∅); (s)% ⊦ dom ∅ = ∅; (s)% ⊦ ¬ n ∈ ∅; (s) Used terms: istore, (dom istore).max + 1