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Proof step 19 from proof ex-lst-shift (previous step)

(o[_∃ xv] * R)[rs, cf, af] ⊦ ∃ x. (o[xv(x)] * R)[rs, cf, af]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ (R0 * R1)[rs, cf, af] ↔ (∃ rs0, rs1. rs0 ∪ rs1 = rs ∧ rs0 ∩ rs1 = ∅ ∧ R0[rs0, cf, af] ∧ R1[rs1, cf, af])

Rule argument

[x0lemmaarg: spec-name: heap-fun instance-name: cell-heap-aux-heap-aux lemma-name: sep antecedent: succedent: (R0 * R1)[rs, cf, af] ↔ (∃ rs0, rs1. rs0 ∪ rs1 = rs ∧ rs0 ∩ rs1 = ∅ ∧ R0[rs0, cf, af] ∧ R1[rs1, cf, af]) substlist: [af, cf, rs, R1, R0] → [af, cf, rs, R, o[_∃ xv]] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (af, cf, rs, R, o[_∃ xv])]]