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Proof step 1 from proof append-cancel-r-01 (conclusion)

⊦ finp(σ) → (⌜x⌝ + σ = ⌜y⌝ + σ ↔ ⌜x⌝ = ⌜y⌝ )

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: eq-stream-to-list-2-2: ⊦ ⌜x⌝ + ⌜y⌝ = ⌜x0⌝ + ⌜z⌝ ↔ x + y = x0 + z;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%a: ⊦ (x + y) + z = x + y + z; from specification list%app-03: ⊦ x + y = z + y ↔ x = z; from specification list%stream-fin-forward: ⊦ finp(σ) → (∃ x. ⌜x⌝ = σ); (forward) from specification stream-basic%inj-02: ⊦ ⌜x⌝ = ⌜x0⌝ ↔ x = x0; from specification stream-basic