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Proof step 7 from proof subset-put-strong-04 (previous step)

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

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: a1 = a

Additional information

Used simplifier rules: At-same: ⊦ st[a, d][a] = d;%At-other: ⊦ a ≠ b → st[b, d][a] = st[a];%in-neq: ⊦ a ≠ b → (a ∈ st[b, d] ↔ a ∈ st);%subset-elem-eq-02: ⊦ b ∈ st ∧ st ⊆ st1 → (st[b] ≠ st1[b] ↔ false); Used formulas: a1 = a