[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 2 from proof min-del (previous step)

s.min ∈ s, s.max ∈ s ⊦ (s -- a).min = s.min, a = s.min, s = ∅, # s = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
a ∈ s, ∀ b. b ∈ s → ¬ b < a ⊦ a = s.min

Rule argument

spec: oset inst: name: min-q seq: a ∈ s, ∀ b. b ∈ s → ¬ b < a ⊦ a = s.min subst: [a, s] → [s.min, s -- a] flags: rewrite, current

Additional information

Used simplifier rules: Max-max: ⊦ a ∈ s → ¬ s.max < a;%Min-min: ⊦ a ∈ s → ¬ a < s.min;%Delete: ⊦ a ∈ s -- b ↔ a ≠ b ∧ a ∈ s; from specification set-union%del-rax: ⊦ a ∈ s -- b ↔ ¬ ¬(a ≠ b ∧ a ∈ s); from specification set-union Used terms: s.min, s -- a