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Proof step 33 from proof del-exists (previous step)

st0 = st[a0, st0[a0]], a0 ∈ st0, ∀ a. a ∈ st0 → (∃ st1. ¬ a ∈ st1 ∧ st0 = st1[a, st0[a]]) ⊦ a = a0, st0[a] = st[a], a0 ∈ st, ∃ st1. ¬ a0 ∈ st1 ∧ st0[a0, d] = st1[a0, d]

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

Used simplifier rules: At-other: ⊦ a ≠ b → st[b, d][a] = st[a];