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Proof step 81 from proof hasSharing-dd-help (previous step)

∃ 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
# refs1 + # refs3 = # refs2, # sks0 = 2 + # refs2 + # refs0, # refs4 = # refs0, st[r -- firstn(1 + # refs0, sks0)] .refval = (refs4 + refs3)[# refs0], fits(r, sks0, st), validrefs(str, (r ' + refs0) + (refs4 + refs3)[# refs0] ' + refs2 + r0 ', st[r -- _type] .type, st), validrefs(str, (r ' + refs4 + refs3) + r1 ' + refs1 + r0 ', st[r -- _type] .type, st) ⊦ refs3 = [], refs4 + refs3 = [], r0 = jvmref, r1 = r0, (refs4 + refs3)[# refs0] = r1, hasSharing(r, st), path∃(str, r1, (refs4 + refs3)[# refs0], st), path∃(str, (refs4 + refs3)[# refs0], r1, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m < m + n ↔ n ≠ 0], [CSIMPSEQ : ⊦ # refs = 0 ↔ refs = []], [CSIMPSEQ : ⊦ m = m + n ↔ n = 0], [CSIMPSEQ : ⊦ m < n → n ≠ 0], [CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n ∧ m = n0 → n0 < n], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0])]]