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Proof step 37 from proof validrefs-putbyte-field (previous step)

refs1 = r1 + refs, r1 = st[r0 -- i '] .refval, is_array(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), st[r0 -- _type] .type ≤ ty, i < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval, is_referencevalue(st[r0 -- i ']), validrefs(str, refs1, st[r0 -- _type] .type .type, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), 0 ≤ i, 0 < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval, ∀ by, fieldvar, class, r, st, ty, str, refs0. # refs0 < # (r0 + refs1) → ( validrefs(str, refs0, ty, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]) → refs0 = [] ∨ junkref(str, refs0 .first, st) ∨ validrefs(str, refs0, ty, st)) ⊦ refs1 = [], r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + refs1, ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
0 ≤ i, 0 < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval, is_array(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), st[r0 -- _type] .type ≤ ty, i < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval, is_referencevalue(st[r0 -- i ']), validrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), ∀ by, fieldvar, class, r, st0, ty, str, refs0. # refs0 < # (r0 + st[r0 -- i '] .refval + refs) → ( validrefs(str, refs0, ty, st0[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]) → refs0 = [] ∨ junkref(str, refs0 .first, st0) ∨ validrefs(str, refs0, ty, st0)) ⊦ r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + st[r0 -- i '] .refval ' + refs, ty, st)

Rule argument

[emptyarg]

Additional information

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