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Proof step 10 from proof subset-put-strong-05 (previous step)

a2 ∈ st[a, d], a2 ∈ st0[a, d], st ⊆ st0 ⊦ st[a, d][a2] = st0[a, d][a2], a2 = a0, a2 = a1

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: a2 = a

Additional information

Used simplifier rules: At-same: ⊦ st[a, d][a] = d;%At-other: ⊦ a ≠ b → st[b, d][a] = st[a];%In-insert: ⊦ a ∈ st[b, d] ↔ a = b ∨ a ∈ st;%subset-elem-eq-02: ⊦ b ∈ st ∧ st ⊆ st1 → (st[b] = st1[b] ↔ true); Used formulas: a2 = a