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Proof step 1 from proof append-to-gr-01 (conclusion)

⊦ # x < m → ⌜x⌝ + σ to m = ⌜x⌝ + (σ to (m - # x))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
# x < m ⊦ ⌜x⌝ + σ to m = ⌜x⌝ + (σ to (m - # x)), m = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1