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Proof step 12 from proof validrefs-applast-class (previous step)

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), validrefs(str, r ' + st[r -- mkfs(class, ty0, fieldvar) '] .refval ', st[r -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 11:
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))

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st, st[r -- _type] .type, st[r -- mkfs(class, ty0, fieldvar) '] .refval ', r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ ty])], [EXTRATERMS : (st, st[r -- _type] .type, st[r -- mkfs(class, ty0, fieldvar) '] .refval ', r, str)]]