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Proof step 23 from proof Sep-forall (previous step)

(aP0 ⊗_ s)(H), ∀ a, H. a ∈ s ∧ aP0(a)(H) → aP(a)(H) ⊦ (aP ⊗_ s)(H)

User applied rule induction

And obtained the following new goals

Proof step 22:
(aP0 ⊗_ s)(H) ∧ (∀ a, H. a ∈ s ∧ aP0(a)(H) → aP(a)(H)), ∀ s0, aP0, H, aP. # s0 < # s → ((aP0 ⊗_ s0)(H) ∧ (∀ a, H. a ∈ s0 ∧ aP0(a)(H) → aP(a)(H)) → (aP ⊗_ s0)(H)) ⊦ (aP ⊗_ s)(H)

Rule argument

[INDHYPARG : [STANDARDINDUCTIONTYPE : ], true, false, # s, [] → [], <]

Additional information

[[CONCRETESIMPRULES : ([CSIMPLESSPRED : <])], [EXTRATERMS : (# s)]]