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Proof step 17 from proof hassharing-validrefs-dups (previous step)

# sks = 1 + # refs1, validrefs(str, r ' + refs1 + r ', st[r -- _type] .type, st), path∃(str, r, r, st), fits(r, sks, st), # sks ≠ 0 ∧ ¬ # sks < # sks → st[r -- firstn(# sks, sks)] .refval = (r ' + refs1 + r ')[# sks], ∀ n. n ≠ 0 ∧ ¬ # sks < n → st[r -- firstn(n, sks)] .refval = (r ' + refs1 + r ')[n], ∀ st, str, refs2, r0. # (r0 ' + refs2) < # (r ' + refs1 + (r + refs)) → (validrefs(str, r0 ' + refs2, st[r0 -- _type] .type, st) → hasSharing(r0, st) ∨ ¬ r0 ∈ refs2 ∧ ¬ dups(refs2)) ⊦ ∃ sks1, sks2. fits(r, sks1, st) ∧ fits(r, sks2, st) ∧ sks1 ≠ sks2 ∧ sks1 ≠ [] ∧ sks2 ≠ [] ∧ st[r -- sks1] .refval ≠ jvmref ∧ st[r -- sks1] = st[r -- sks2]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
# sks = 1 + # refs1, st[r -- sks] .refval = (r ' + refs1 + r ')[# sks], validrefs(str, r ' + refs1 + r ', st[r -- _type] .type, st), path∃(str, r, r, st), fits(r, sks, st), ∀ n. n ≠ 0 ∧ ¬ # sks < n → st[r -- firstn(n, sks)] .refval = (r ' + refs1 + r ')[n], ∀ st, str, refs2, r0. # (r0 ' + refs2) < # (r ' + refs1 + (r + refs)) → (validrefs(str, r0 ' + refs2, st[r0 -- _type] .type, st) → hasSharing(r0, st) ∨ ¬ r0 ∈ refs2 ∧ ¬ dups(refs2)) ⊦ sks = [], ∃ sks1, sks2. fits(r, sks1, st) ∧ fits(r, sks2, st) ∧ sks1 ≠ sks2 ∧ sks1 ≠ [] ∧ sks2 ≠ [] ∧ st[r -- sks1] .refval ≠ jvmref ∧ st[r -- sks1] = st[r -- sks2]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ # [] = 0], [CSIMPSEQ : ⊦ firstn(# sks, sks) = sks], [CSIMPSEQ : ⊦ ¬ n < n], [CSIMPSEQ : ⊦ # sks = 0 ↔ sks = []])]]