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Proof step 53 from proof hasSharing-dd-help (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 52:
# refs + # refs1 = # refs2 + # refs0, # sks0 = 2 + # refs2 + # refs0, fits(r, sks0, st), validrefs(str, (r ' + refs0) + r2 ' + refs2 + r0 ', st[r -- _type] .type, st), validrefs(str, (r ' + refs) + st[r -- firstn(1 + # refs, sks0)] .refval ' + refs1 + r0 ', st[r -- _type] .type, st), # refs < # refs0, 1 + # refs ≠ 0 ∧ ¬ # sks0 < 1 + # refs → st[r -- firstn(1 + # refs, sks0)] .refval = ((r ' + refs0) + r2 ' + refs2 + r0 ')[1 + # refs] ⊦ r0 = jvmref, st[r -- firstn(1 + # refs, sks0)] .refval = r0, r2 = st[r -- firstn(1 + # refs, sks0)] .refval, # refs = # refs0, refs0 = [], hasSharing(r, st), path∃(str, st[r -- firstn(1 + # refs, sks0)] .refval, r2, st), path∃(str, r2, st[r -- firstn(1 + # refs, sks0)] .refval, st)

Rule argument

[EXRARG : pos: left 7, [extquanttermlist: (1 + # refs) abort:F , discard:T , computed:T ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (1 + # refs)]]