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Proof step 2 from proof restrict-intersect-empty-write-add (previous step)

dom st ∩ s = ∅ ⊦ st[a, d] \ (s -- a) = st[a, d]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ dom st ∩ s = ∅ → st \ s = st

Rule argument

spec: inst: name: restrict-intersect-empty seq: ⊦ dom st ∩ s = ∅ → st \ s = st subst: [s, st] → [s -- a, st[a, d]] flags: rewrite, current

Additional information

Used simplifier rules: dom-ins: ⊦ dom st[a, d] = dom st ++ a;%intersect-add-rem: ⊦ (s0 ++ a) ∩ (s1 -- a) = (s0 ∩ s1) -- a; from specification set-union%int-a: ⊦ (s ∩ s0) ∩ s1 = s ∩ s0 ∩ s1; from specification set-union%int-c: ⊦ s ∩ s0 = s0 ∩ s; from specification set-union%del-e-02: ⊦ s -- a = ∅ ↔ s = ∅ ∨ s = ∅ ++ a; from specification set-union Used terms: s -- a, st[a, d]