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Proof step 13 from proof precise-Sep (previous step)

precise(adP(a, d)), a0 ∈ st0, ∀ a0. a0 ∈ st0[a, d] → precise(adP(a0, st0[a, d][a0])), ∀ st1, adP. # st1 < # st0[a, d] → (∀ a. a ∈ st1 → precise(adP(a, st1[a]))) → precise(adP ⊗_ st1) ⊦ precise(adP(a0, st0[a0])), precise(adP(a, d) * adP ⊗_ st0), precise(adP ⊗_ st0), a ∈ st0

User applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: a0 abort: F discard: F computed: F

Additional information

Used simplifier rules: ⊦ b ∈ st ∧ ¬ a ∈ st → st[a, d][b] = st[b]; (s)% ⊦ a ∈ st[b, d] ↔ a = b ∨ a ∈ st; (ws) Used terms: a0