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Proof step 4 from proof get-unknown (previous step)

(a[r =>_] * R)[rs, f, g] ⊦ g(r) = a

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ r =>_ = _∃ λ o. r => o

Rule argument

[x0lemmaarg: spec-name: maplet instance-name: lemma-name: mapex antecedent: succedent: r =>_ = _∃ λ o. r => o substlist: [r] → [r] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0, 1, 0, 1, 0, 1, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : lift-ex-o, , , ⊦ a[_∃ oP] = _∃ λ o, a0. a[oP(o)]], [CSIMPNAMEDSEQ : get-known, , , ⊦ (a[r => o] * R)[rs, f, g] → (g(r) ≠ a ↔ false)], [CSIMPSEQ : ⊦ (_∃ oR * R)[rs, f, g] ↔ (∃ o, a. (oR(o, a) * R)[rs, f, g])], [CSIMPSEQ : ⊦ (R0 * R1) * R2 = R0 * R1 * R2], [CSIMPSEQ : ⊦ R0 * R1 = R1 * R0])], [EXTRATERMS : (r)]]