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Proof step 106 from proof hasSharing-dd-help (previous step)

2 + # refs0 + # refs2 ≠ 0, # sks = 2 + # refs0 + # refs2, # sks0 = 2 + # refs + # refs1, st[r -- sks] .refval = (refs0 + r2 ' + refs2 + r0 ')[(2 + # refs0 + # refs2) -1], validrefs(str, (r ' + refs) + r1 ' + refs1 + r0 ', st[r -- _type] .type, st), validrefs(str, (r ' + refs0) + r2 ' + refs2 + r0 ', st[r -- _type] .type, st), fits(r, sks, st), fits(r, sks0, st), ∀ n. n ≠ 0 ∧ ¬ 2 + # refs0 + # refs2 < n → st[r -- firstn(n, sks)] .refval = ((r ' + refs0) + r2 ' + refs2 + r0 ')[n], ∀ n. n ≠ 0 ∧ ¬ # sks0 < n → st[r -- firstn(n, sks0)] .refval = ((r ' + refs) + r1 ' + refs1 + r0 ')[n] ⊦ sks = sks0, r2 = r1, r1 = r0, r0 = jvmref, sks0 = [], sks = [], path∃(str, r2, r1, st), path∃(str, r1, r2, st), st[r -- sks] = st[r -- sks0] ∧ st[r -- sks] .refval ≠ jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 105:
# sks0 = 2 + # refs + # refs1, # sks = 2 + # refs0 + # refs2, fits(r, sks0, st), fits(r, sks, st), validrefs(str, (r ' + refs0) + r2 ' + refs2 + st[r -- sks] .refval ', st[r -- _type] .type, st), validrefs(str, (r ' + refs) + r1 ' + refs1 + st[r -- sks] .refval ', st[r -- _type] .type, st), ∀ n. n ≠ 0 ∧ ¬ # sks0 < n → st[r -- firstn(n, sks0)] .refval = ((r ' + refs) + r1 ' + refs1 + st[r -- sks] .refval ')[n], ∀ n. n ≠ 0 ∧ ¬ # sks < n → st[r -- firstn(n, sks)] .refval = ((r ' + refs0) + r2 ' + refs2 + st[r -- sks] .refval ')[n] ⊦ sks = [], sks0 = [], st[r -- sks] .refval = jvmref, r1 = st[r -- sks] .refval, r2 = r1, sks = sks0, st[r -- sks] = st[r -- sks0], path∃(str, r1, r2, st), path∃(str, r2, r1, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : n < n0 ⊦ ((* n)) ≠ m0 + ((* n0))], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (refs + r ')[# refs] = r], [CSIMPSEQ : ⊦ (r ' + refs)[n + 1] = refs[n]], [CSIMPSEQ : ⊦ (refs + refs0)[n + # refs] = refs0[n]], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ n ≤ m → m + n0 - n = (m - n) + n0], [CSIMPSEQ : ⊦ n -1 = n - 1])]]