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Proof step 18 from proof all-classes-02 (previous step)

rk ∈ rks, r -- fs ' ∈ rks, # str ≤ # fs .class .class, ∀ rk0. rk0 ≠ rk ∧ rk0 ∈ rks ∧ is_fskey(rk0 .key) → # rk0 .key .fs .class .class < # str, ∀ rks0. # rks0 < # rks → (true → (∃ str. ∀ rk. rk ∈ rks0 ∧ is_fskey(rk .key) → ¬ # str ≤ # rk .key .fs .class .class)) ⊦ # rks = 0, rks = ∅, ∃ str. ∀ rk. rk ∈ rks ∧ is_fskey(rk .key) → ¬ # str ≤ # rk .key .fs .class .class

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
fs = mkfs(class, ty, fieldvar), rk ∈ rks, r -- fs ' ∈ rks, # str ≤ # class .class, ∀ rk0. rk0 ≠ rk ∧ rk0 ∈ rks ∧ is_fskey(rk0 .key) → # rk0 .key .fs .class .class < # str, ∀ rks0. # rks0 < # rks → (true → (∃ str. ∀ rk. rk ∈ rks0 ∧ is_fskey(rk .key) → ¬ # str ≤ # rk .key .fs .class .class)) ⊦ # rks = 0, rks = ∅, ∃ str. ∀ rk. rk ∈ rks ∧ is_fskey(rk .key) → ¬ # str ≤ # rk .key .fs .class .class

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [fs, class, ty, fieldvar] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (fs, class, ty, fieldvar)]]