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Proof step 4 from proof all-classes-02 (previous step)

# str < # class .class, r0 -- mkfs(class, ty0, fieldvar0) ' ∈ rks, # str ≤ # stringvar, r -- mkfs(stringvar .class, ty, fieldvar) ' ∈ rks, # stringvar < # class .class, ∀ rk0. rk0 ≠ r -- mkfs(stringvar .class, ty, fieldvar) ' ∧ 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 = ∅, # rks = 0, ∃ 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 3:
class = stringvar0 .class, # str < # stringvar0, r0 -- mkfs(class, ty0, fieldvar0) ' ∈ rks, # str ≤ # stringvar, r -- mkfs(stringvar .class, ty, fieldvar) ' ∈ rks, # stringvar < # stringvar0, ∀ rk0. rk0 ≠ r -- mkfs(stringvar .class, ty, fieldvar) ' ∧ 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 = ∅, # rks = 0, ∃ str. ∀ rk. rk ∈ rks ∧ is_fskey(rk .key) → ¬ # str ≤ # rk .key .fs .class .class

Rule argument

[speclemmaarg: ,stringvar = class .class ↔ class = stringvar .class ,[class, stringvar] → [class, stringvar0] ,T ,classname , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ stringvar = class .class ↔ class = stringvar .class])], [EXTRATERMS : (class, stringvar0)]]