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Proof step 18 from proof butmin-put-01 (previous step)

a = st[a, d0].min ⊦ a0 = a, a0 = st[a, d].min, a0 ∈ st[a, d] -- st[a, d].min ↔ a0 ∈ st, a ∈ st

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 3

Additional information

Used simplifier rules: min-put-01: ⊦ st[a, d].min = a → st[a, d0].min = a;%min-put-01: ⊦ st[a, d].min = a → st[a, d0].min = a;%insert: ⊦ st[a, d] -- a = st -- a; from specification store%notin-del-notin: ⊦ ¬ a ∈ st → st -- a = st; from specification store