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Proof step 13 from proof validrefs-applast-class (previous step)

validrefs(str, refs + r ', ty, st) ∧ validrefs(str, r ' + st[r -- mkfs(class, ty0, fieldvar) '] .refval ', st[r -- _type] .type, st) ∧ (refs + r ') .last = (r ' + st[r -- mkfs(class, ty0, fieldvar) '] .refval ') .first ∧ refs + r ' ≠ [] ∧ r ' + st[r -- mkfs(class, ty0, fieldvar) '] .refval ' ≠ [] → validrefs(str, (refs + r ') + (r ' + st[r -- mkfs(class, ty0, fieldvar) '] .refval ') .rest, ty, st), 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .rest = refs], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ (refs + r ') .last = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]