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Proof step 11 from proof butmin-put-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
a = st[a, d0].min ⊦ a = st[a, d].min, a ∈ st, ¬ a ∈ st[a, (∅)[a]] -- st[a, (∅)[a]].min ∧ d = (∅)[a]

Rule argument

Additional information

Used simplifier rules: notmemlookup: ⊦ ¬ a ∈ st → st[a] = (∅)[a]; from specification store%At-same: ⊦ st[a, d][a] = d; from specification store