[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 9 from proof all-classes-02 (previous step)

rk = r0 -- sk, # str < # sk .fs .class .class, # stringvar < # sk .fs .class .class, r -- mkfs(stringvar .class, ty, fieldvar) ' ∈ rks, # str ≤ # stringvar, is_fskey(sk), rk ∈ rks, ∀ rk0. rk0 ≠ r -- mkfs(stringvar .class, ty, fieldvar) ' ∧ rk0 ∈ rks ∧ is_fskey(rk0 .key) → # rk0 .key .fs .class .class < # str, ∀ rks0. # rks0 < # rks → (true → (∃ str. ∀ rk. rk ∈ rks0 ∧ is_fskey(rk .key) → ¬ # str ≤ # rk .key .fs .class .class)) ⊦ # rks = 0, rks = ∅, ∃ str. ∀ rk. rk ∈ rks ∧ is_fskey(rk .key) → ¬ # str ≤ # rk .key .fs .class .class

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
# str < # sk .fs .class .class, r0 -- sk ∈ rks, is_fskey(sk), # str ≤ # stringvar, r -- mkfs(stringvar .class, ty, fieldvar) ' ∈ rks, # stringvar < # sk .fs .class .class, ∀ rk0. rk0 ≠ r -- mkfs(stringvar .class, ty, fieldvar) ' ∧ rk0 ∈ rks ∧ is_fskey(rk0 .key) → # rk0 .key .fs .class .class < # str, ∀ rks0. # rks0 < # rks → (true → (∃ str. ∀ rk. rk ∈ rks0 ∧ is_fskey(rk .key) → ¬ # str ≤ # rk .key .fs .class .class)) ⊦ rks = ∅, # rks = 0, ∃ str. ∀ rk. rk ∈ rks ∧ is_fskey(rk .key) → ¬ # str ≤ # rk .key .fs .class .class

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m ≤ n ∧ n < n0 → m < n0])]]