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Proof step 13 from proof all-classes-02 (previous step)

rk ∈ rks, r -- mkfs(stringvar .class, ty, fieldvar) ' ∈ rks, # str ≤ # stringvar, r -- mkfs(stringvar .class, ty, fieldvar) ' ≠ rk ∧ r -- mkfs(stringvar .class, ty, fieldvar) ' ∈ rks ∧ is_fskey((r -- mkfs(stringvar .class, ty, fieldvar) ') .key) → # (r -- mkfs(stringvar .class, ty, fieldvar) ') .key .fs .class .class < # str, ∀ 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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# str ≤ # stringvar, r -- mkfs(stringvar .class, ty, fieldvar) ' ∈ rks, ∀ 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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : ⊦ ¬ n < n], [CSIMPSEQ : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n ∧ n ≤ n0 → m < n0], [CSIMPFORWARD : ⊦ m ≤ n ∧ n < n0 → m < n0], [CSIMPSEQ : ⊦ stringvar .class .class = stringvar], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .class = class], [CSIMPSEQ : ⊦ fs ' .fs = fs], [CSIMPSEQ : ⊦ is_fskey(fs ')], [CSIMPSEQ : ⊦ (r -- sk) .key = sk])]]