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Proof step 24 from proof ex-validrefs-fits-stronger (previous step)

refs0 = r0 + refs1, r0 = st[r -- mkfs(class, ty0, fieldvar) '] .refval, is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), validrefs(str, refs0, ty0, st), ∀ st, ty, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, ty, st) → (∃ sks. fits(r, sks, st) ∧ # sks = # refs ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st[r -- firstn(n, sks)] .refval = (r ' + refs)[n]))) ⊦ refs0 = [], r = jvmref, ∃ sks. fits(r, sks, st) ∧ # sks = # refs0 ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st[r -- firstn(n, sks)] .refval = (r ' + refs0)[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), validrefs(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs1, ty0, st), ∀ st0, ty, r1, str, refs. # refs < # (st[r -- mkfs(class, ty0, fieldvar) '] .refval + refs1) → ( validrefs(str, r1 ' + refs, ty, st0) → (∃ sks. fits(r1, sks, st0) ∧ # sks = # refs ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st0[r1 -- firstn(n, sks)] .refval = (r1 ' + refs)[n]))) ⊦ r = jvmref, ∃ sks. fits(r, sks, st) ∧ # sks = 1 + # refs1 ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st[r -- firstn(n, sks)] .refval = (r ' + st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs1)[n])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]