[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 bmin-bin (previous step)

s.min ∈ s, s.max ∈ s ⊦ # s = 1, s = ∅, # s = 0, (s -- s.min).min ∈ s

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ s ≠ ∅ ∧ s ⊆ s0 → s.min ∈ s0

Rule argument

spec: oset inst: name: min-subset seq: ⊦ s ≠ ∅ ∧ s ⊆ s0 → s.min ∈ s0 subst: [s0, s] → [s, s -- s.min] flags: rewrite, current

Additional information

Used simplifier rules: del-e-02: ⊦ s -- a = ∅ ↔ s = ∅ ∨ s = ∅ ++ a; from specification set-union%sub-del-02: ⊦ s -- a ⊆ s; from specification set-union%one-min: ⊦ s = ∅ ++ a → s -- a = ∅; from specification set-union%one-size: ⊦ s = ∅ ++ a → # s = 1; (forward) from specification set-basic%in-06: ⊦ a ∈ s ∧ s = ∅ ++ b → a = b; (forward) from specification set-basic Used terms: s, s -- s.min