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Proof step 3 from proof gfts-in (previous step)

∀ sk, r, st. sk ∈ sks0 ∧ goodfieldsandtypes(r, sks0, st) → goodfieldandtype(r, sk, st) ⊦ sk0 ∈ sk + sks0 ∧ goodfieldsandtypes(r, sk + sks0, st) → goodfieldandtype(r, sk0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ goodfieldsandtypes(r, sk ' + sks, st) ↔ goodfieldandtype(r, sk, st) ∧ goodfieldsandtypes(r, sks, st)
Proof step 2:
goodfieldandtype(r, sk, st), goodfieldsandtypes(r, sks0, st), sk0 ∈ sks0, ∀ sk, r, st. sk ∈ sks0 ∧ goodfieldsandtypes(r, sks0, st) → goodfieldandtype(r, sk, st) ⊦ goodfieldandtype(r, sk0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk + sks = sk ' + sks], [CSIMPSEQ : ⊦ sk ∈ sks + sks0 ↔ ¬ ¬ (sk ∈ sks ∨ sk ∈ sks0)], [CSIMPSEQ : ⊦ sk ∈ sk0 ' ↔ sk = sk0], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1])]]