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Proof step 28 from proof validrefs-subset-equiv (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), r ∈ st, is_obj(str, r, st), st[r -- _type] .type ≤ ty, st ⊆ st0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r0 ' + refs1, ty0, st0), r -- _type ∈ st, r -- mkfs(class, ty0, fieldvar) ' ∈ st, ∀ st, st1, ty, r1, str, refs0. # refs0 < # (r0 + refs1) → (validrefs(str, r1 ' + refs0, ty, st1) ∧ st ⊆ st1 ∧ validref(str, r1, st[r1 -- _type] .type, st) → validrefs(str, r1 ' + refs0, ty, st)) ⊦ r = jvmref, junkref(str, r, st), validrefs(str, r0 ' + refs1, ty0, st)

User applied rule apply induction

And obtained the following new goals

Proof step 27:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), r ∈ st, is_obj(str, r, st), st[r -- _type] .type ≤ ty, st ⊆ st0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r0 ' + refs1, ty0, st0), r -- _type ∈ st, r -- mkfs(class, ty0, fieldvar) ' ∈ st, ∀ st, st1, ty, r1, str, refs0. # refs0 < # (r0 + refs1) → (validrefs(str, r1 ' + refs0, ty, st1) ∧ st ⊆ st1 ∧ validref(str, r1, st[r1 -- _type] .type, st) → validrefs(str, r1 ' + refs0, ty, st)) ⊦ validrefs(str, r0 ' + refs1, ty0, st0) ∧ st ⊆ st0 ∧ validref(str, r0, st[r0 -- _type] .type, st), r = jvmref, junkref(str, r, st), validrefs(str, r0 ' + refs1, ty0, st)

Rule argument

[substlist-arg: [st, st1, ty, r1, str, refs0] → [st, st0, ty0, r0, str, refs1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r + refs = r ' + refs], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ ¬ n < n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (st, st0, ty0, r0, str, refs1)]]