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Proof step 2 from proof cons-eq (previous step)

⌜a '⌝ + σ = ⌜a0 '⌝ + σ0 ⊦ a = a0 ∧ σ = σ0

User applied rule structural induction

And obtained the following new goals

Proof step 3:
⌜a '⌝ + ⌜x⌝ = ⌜a0 '⌝ + σ0 ⊦ a = a0 ∧ ⌜x⌝ = σ0
Proof step 4:
⌜a '⌝ + ⌜nf⌝ = ⌜a0 '⌝ + σ0 ⊦ a = a0 ∧ ⌜nf⌝ = σ0

Rule argument

indvar: σ

Additional information

Used simplifier rules: stream freely generated by ⌜ ⌝, ⌜ ⌝;;