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Proof step 44 from proof del-exists (previous step)

∀ a0. a0 ∈ st[a, st0[a]] → (∃ st1. ¬ a0 ∈ st1 ∧ st[a, st0[a]] = st1[a0, st[a, st0[a]][a0]]) ⊦ a1 = a0, a = a0, a ∈ st, ∃ st1. ¬ a ∈ st1 ∧ st[a, st0[a]][a0, d] = st1[a, st0[a]], (a1 ∈ st[a, st0[a]] ↔ a1 ∈ st[a0, d][a, st0[a]]) ∧ st[a, st0[a]][a1] = st[a0, d][a, st0[a]][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;%In-insert: ⊦ a ∈ st[b, d] ↔ a = b ∨ a ∈ st;%in-neq: ⊦ a ≠ b → (a ∈ st[b, d] ↔ a ∈ st);%At-other: ⊦ a ≠ b → st[b, d][a] = st[a]; Used formulas: a1 = a