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Proof step 4 from proof Del-notin (previous step)

a ∈ st0[a0, d] -- a, ∀ a. ¬ a ∈ st0 -- a ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ a ≠ b → st[b, d] -- a = (st -- a)[b, d]
Proof step 6:
a = a0, a ∈ st0[a0, d] -- a, ∀ a. ¬ a ∈ st0 -- a ⊦
Proof step 8:
a ∈ (st0 -- a)[a0, d], ∀ a. ¬ a ∈ st0 -- a ⊦ a = a0

Rule argument

spec: <toplevel> name: Del-rec-other seq: ⊦ a ≠ b → st[b, d] -- a = (st -- a)[b, d] subst: [a, d, b, st] → [a, d, a0, st0] flags: <all paths>

Additional information

Used terms: a, d, a0, st0