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Proof step 11 from proof validrefs-applast-class (previous step)

is_obj(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, validrefs(str, refs + r ', ty, st), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), is_obj(str, r, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[st[r -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type ≤ ty0, is_valid_ref(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval, st), type∃(str, st[st[r -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type) ⊦ validrefs(str, refs + r ' + st[r -- mkfs(class, ty0, fieldvar) '] .refval ', ty, st), st[r -- mkfs(class, ty0, fieldvar) '] .refval ' = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- mkfs(class, ty0, fieldvar) '] .refval ' .first = st[r -- fs '] .refval ∧ validrefs(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval ', fs .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
validrefs(str, refs + r ', ty, st), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), is_obj(str, r, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[st[r -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type ≤ ty0, is_valid_ref(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval, st), type∃(str, st[st[r -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type) ⊦ validrefs(str, refs + r ' + st[r -- mkfs(class, ty0, fieldvar) '] .refval ', ty, st), ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- mkfs(class, ty0, fieldvar) '] .refval = st[r -- fs '] .refval ∧ validrefs(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval ', fs .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ' .first = r], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ r ' ≠ []])]]