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Proof step 38 from proof validval-putrkvs (previous step)

sk .fs = mkfs(class, ty, fieldvar), validvals(str, rkvs, st), ¬ is_fskey(sk) → validval(str, val, st[r -- _type] .type .type, st), ¬ is_indexkey(sk) → validval(str, val, ty, st) ∧ ty ≠ void_type ∧ sk ≠ _length ⊦ (is_fskey(sk) → validval(str, val, ty, st[rkvs]) ∧ ty ≠ void_type ∧ sk ≠ _length) ∧ (is_indexkey(sk) → validval(str, val, (st[rkvs][r -- _type]) .type .type, st[rkvs]))

User applied rule case distinction

And obtained the following new goals

Proof step 18:
sk .fs = mkfs(class, ty, fieldvar), validvals(str, rkvs, st), ¬ is_fskey(sk) → validval(str, val, st[r -- _type] .type .type, st), ¬ is_indexkey(sk) → validval(str, val, ty, st) ∧ ty ≠ void_type ∧ sk ≠ _length ⊦ is_fskey(sk) → validval(str, val, ty, st[rkvs]) ∧ ty ≠ void_type ∧ sk ≠ _length
Proof step 37:
sk .fs = mkfs(class, ty, fieldvar), validvals(str, rkvs, st), ¬ is_fskey(sk) → validval(str, val, st[r -- _type] .type .type, st), ¬ is_indexkey(sk) → validval(str, val, ty, st) ∧ ty ≠ void_type ∧ sk ≠ _length ⊦ is_indexkey(sk) → validval(str, val, (st[rkvs][r -- _type]) .type .type, st[rkvs])

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]