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Proof step 82 from proof hasSharing-dd-help (previous step)

st[r -- firstn(1 + # refs0, sks0)] .refval = refs[# refs0], # refs + # refs1 = # refs2 + # refs0, # sks0 = 2 + # refs2 + # refs0, # refs0 < # refs, fits(r, sks0, st), validrefs(str, (r ' + refs0) + refs[# refs0] ' + refs2 + r0 ', st[r -- _type] .type, st), validrefs(str, (r ' + refs) + r1 ' + refs1 + r0 ', st[r -- _type] .type, st) ⊦ r0 = jvmref, r1 = r0, refs[# refs0] = r1, # refs = # refs0, refs = [], hasSharing(r, st), path∃(str, r1, refs[# refs0], st), path∃(str, refs[# refs0], r1, st)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 63:
n ≤ # refs ⊦ ∃ refs0, refs1. refs = refs0 + refs1 ∧ # refs0 = n
Proof step 81:
∃ refs2, refs1. refs = refs2 + refs1 ∧ # refs2 = # refs0, st[r -- firstn(1 + # refs0, sks0)] .refval = refs[# refs0], # refs + # refs1 = # refs2 + # refs0, # sks0 = 2 + # refs2 + # refs0, # refs0 < # refs, fits(r, sks0, st), validrefs(str, (r ' + refs0) + refs[# refs0] ' + refs2 + r0 ', st[r -- _type] .type, st), validrefs(str, (r ' + refs) + r1 ' + refs1 + r0 ', st[r -- _type] .type, st) ⊦ r0 = jvmref, r1 = r0, refs[# refs0] = r1, # refs = # refs0, refs = [], hasSharing(r, st), path∃(str, r1, refs[# refs0], st), path∃(str, refs[# refs0], r1, st)

Rule argument

[speclemmaarg: n ≤ # refs ,∃ refs0, refs1. refs = refs0 + refs1 ∧ # refs0 = n ,[n, refs] → [# refs0, refs] ,F ,list ,references ,split-first ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ m < n → ¬ n < m])], [EXTRATERMS : (# refs0, refs)]]