[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 38 from proof ac-init (previous step)

is_fskey(sk), ∀ class1, st. mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ∨ initdone(class1, addclass(class1, fis0, st)) ⊦ mkfs(class1, void_type, `initstate' .field) ' = sk, initdone(class1, addclass(class1, (sk × val) ' + fis0, st)), mkfs(class1, void_type, `initstate' .field) ' ∈ fis0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is_fskey(fv .1) ∧ fv .1 .fs .class ≠ class → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 31:
¬ (is_fskey((sk × val) .1) ∧ (sk × val) .1 .fs .class ≠ class1), is_fskey(sk), ∀ class1, st. mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ∨ initdone(class1, addclass(class1, fis0, st)) ⊦ mkfs(class1, void_type, `initstate' .field) ' = sk, initdone(class1, addclass(class1, (sk × val) ' + fis0, st)), mkfs(class1, void_type, `initstate' .field) ' ∈ fis0
Proof step 37:
is_fskey((sk × val) .1) ∧ (sk × val) .1 .fs .class ≠ class1, is_fskey(sk), ∀ class1, st. mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ∨ initdone(class1, addclass(class1, fis0, st)) ⊦ mkfs(class1, void_type, `initstate' .field) ' = sk, initdone(class1, addclass(class1, fis0, st)), mkfs(class1, void_type, `initstate' .field) ' ∈ fis0

Rule argument

[crewrite-arg: ac-no1 , F , [st, fis, fv, class] → [st, fis0, sk × val, class1] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, sk × val, class1)]]