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Proof step 12 from proof del-exists (previous step)

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

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard, [[2,1,1,1]]

Additional information

Used simplifier rules: insins: ⊦ st[a, d0][a, d] = st[a, d];%inj-put: ⊦ ¬ a ∈ st ∧ ¬ a ∈ st0 → (st[a, d] = st0[a, d] ↔ st = st0);