[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 17 from proof update-ex-nodups (conclusion)

⊦ ∃ fis0. ¬ dups(fis0 .keys) ∧ update(r, fis, st) = update(r, fis0, st) ∧ fis0 ⊆ fis

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ update(r, [], st) = st
Proof step 2:
⊦ [] .keys = []
Proof step 16:
∀ r, st. ∃ fis1. ¬ dups(fis1 .keys) ∧ update(r, fis0, st) = update(r, fis1, st) ∧ fis1 ⊆ fis0 ⊦ ∃ fis1. ¬ dups(fis1 .keys) ∧ update(r, fv + fis0, st) = update(r, fis1, st) ∧ fis1 ⊆ fv + fis0

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldinits generated by [], +;], [CSIMPSEQ : ⊦ fis ⊆ [] ↔ fis = []], [CSIMPSEQ : ⊦ ¬ dups([])])]]