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Proof step 89 from proof validval-put-any (previous step)

sk .fs = mkfs(class, ty, fieldvar), validref(str, r0, st[r -- _type] .type .type, st), okval(refval(r0), st[r -- _type] .type .type), is_indexkey(sk), validval(str, r1 -- mkfs(class0, ty0, fieldvar0) ', val, st), r ≠ r1 ∨ _type ≠ mkfs(class0, ty0, fieldvar0) ' ⊦ validref(str, r0, st[r -- _type] .type .type, st[r1 -- mkfs(class0, ty0, fieldvar0) ', val]), (is_referencevalue(val) → validref(str, val .refval, ty0, st) ∧ is_reftype(ty0)) ∧ (¬ is_referencevalue(val) → okval(val, ty0) ∧ ty0 ≠ void_type ∧ mkfs(class0, ty0, fieldvar0) ' ≠ _length)

User applied rule case distinction

And obtained the following new goals

Proof step 87:
sk .fs = mkfs(class, ty, fieldvar), validref(str, r0, st[r -- _type] .type .type, st), okval(refval(r0), st[r -- _type] .type .type), is_indexkey(sk), validval(str, r1 -- mkfs(class0, ty0, fieldvar0) ', val, st), r ≠ r1 ∨ _type ≠ mkfs(class0, ty0, fieldvar0) ' ⊦ is_referencevalue(val) → validref(str, val .refval, ty0, st) ∧ is_reftype(ty0), validref(str, r0, st[r -- _type] .type .type, st[r1 -- mkfs(class0, ty0, fieldvar0) ', val])
Proof step 88:
⊦ ¬ is_referencevalue(val) → (validval(str, r -- fs ', val, st) ↔ okval(val, fs .type) ∧ fs ' ≠ _length)

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .type = ty], [CSIMPSEQ : ⊦ okval(val, void_type) ↔ is_referencevalue(val)])]]