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Proof step 1 from proof del-exists (conclusion)

a ∈ st ⊦ ∃ st0. ¬ a ∈ st0 ∧ st = st0[a, st[a]]

User applied rule structural induction

And obtained the following new goals

Proof step 2:
a ∈ st0[a0, d], ∀ a. a ∈ st0 → (∃ st1. ¬ a ∈ st1 ∧ st0 = st1[a, st0[a]]) ⊦ ∃ st1. ¬ a ∈ st1 ∧ st0[a0, d] = st1[a, st0[a0, d][a]]

Rule argument

indvar: st

Additional information

Used simplifier rules: gen: ⊦ ;%In-empty: ⊦ ¬ a ∈ ∅;