[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 22 from proof read-lookup-copy (previous step)

# ax0 = # kx1, new(ax0, fs), key ∈ ri, key1 ∈ ri, key ∈ kx1, kx1.toSet ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]), ∀ kx0, fs0, key0, ri0. # kx1 = # kx0 ∧ new(ax0, fs0) ∧ key0 ∈ ri0 ∧ kx0.toSet ⊆ dom ri0 ∧ (∀ key. key ∈ ri0 → ri0[key] ∈ fs0 ∧ key-cons(key, fs0[ri0[key]])) → fs0[ax0, fs0[ri0[kx0]]][ri0[kx0, ax0][key0]] = fs0[ri0[key0]] ∨ dups(kx0) ⊦ fs[ri[key1]] = fs[ri[key]], dups(ax0), dups(kx1), key1 ∈ kx1, ri[kx1, ax0][key] ∈ ax0, ri[kx1, ax0][key] ∈ fs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ key ∈ kx ↔ (∃ kx0, kx1. kx = kx0 + (key + kx1))
Proof step 24:
# ax0 = # kx1, new(ax0, fs), key1 ∈ ri, key ∈ ri, kx1.toSet ⊆ dom ri, ∀ kx0, fs0, key0, ri0. # kx1 = # kx0 ∧ new(ax0, fs0) ∧ key0 ∈ ri0 ∧ kx0.toSet ⊆ dom ri0 ∧ (∀ key. key ∈ ri0 → ri0[key] ∈ fs0 ∧ key-cons(key, fs0[ri0[key]])) → fs0[ax0, fs0[ri0[kx0]]][ri0[kx0, ax0][key0]] = fs0[ri0[key0]] ∨ dups(kx0), ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]), ∃ kx0, kx2. kx1 = kx0 + (key + kx2) ⊦ fs[ri[key1]] = fs[ri[key]], dups(kx1), dups(ax0), ri[kx1, ax0][key] ∈ fs, ri[kx1, ax0][key] ∈ ax0, key1 ∈ kx1

Rule argument

spec: list, inst: key-list-set name: in-def seq: ⊦ key ∈ kx ↔ (∃ kx0, kx1. kx = kx0 + (key + kx1)) subst: [kx, key] → [kx1, key] flags: <all paths>

Additional information

Used terms: kx1, key