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Proof step 6 from proof encode-contract (previous step)

buf0 = buf, EB_PAGE_SIZE ≤ # buf, ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE, ENCODED_ELEM_SIZE ≤ # buf ⊦ ⟪encode_nonempty#(a, 0; buf; err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ (err = ESUCCESS → is-encoded-pagesize(a, subarray(buf, 0, EB_PAGE_SIZE))))

User applied rule insert program lemma

And obtained the following new goals

Proof step 7:
n + ENCODED_ELEM_SIZE ≤ # buf, buf0 = buf ⊦ ⟪encode_nonempty#(a, n; buf; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ subarray(buf, 0, n) = subarray(buf0, 0, n) ∧ subarray(buf, n + ENCODED_ELEM_SIZE, # buf - n + ENCODED_ELEM_SIZE) = subarray(buf0, n + ENCODED_ELEM_SIZE, # buf - n + ENCODED_ELEM_SIZE) ∧ (err = ESUCCESS → is-encoded-nonempty(a, subarray(buf, n, ENCODED_ELEM_SIZE))))
Proof step 8:
a0 = a, buf = buf, buf0 = buf, buf1 = buf, n0 = 0, ENCODED_ELEM_SIZE ≤ # buf, ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE, EB_PAGE_SIZE ≤ # buf, 0 + ENCODED_ELEM_SIZE ≤ # buf ⊦ [encode_nonempty#(a, 0; buf; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf1 ∧ subarray(buf, 0, n0) = subarray(buf1, 0, n0) ∧ subarray(buf, n0 + ENCODED_ELEM_SIZE, # buf - n0 + ENCODED_ELEM_SIZE) = subarray(buf1, n0 + ENCODED_ELEM_SIZE, # buf - n0 + ENCODED_ELEM_SIZE) ∧ (err = ESUCCESS → is-encoded-nonempty(a0, subarray(buf, n0, ENCODED_ELEM_SIZE))) → (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ (err = ESUCCESS → is-encoded-pagesize(a, subarray(buf, 0, EB_PAGE_SIZE))))

Rule argument

spec: encoding-fixed-size-nonempty name: encode-contract seq: n + ENCODED_ELEM_SIZE ≤ # buf, buf0 = buf ⊦ ⟪encode_nonempty#(a, n; buf; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ # buf = # buf0 ∧ subarray(buf, 0, n) = subarray(buf0, 0, n) ∧ subarray (buf, n + ENCODED_ELEM_SIZE, # buf - n + ENCODED_ELEM_SIZE) = subarray (buf0, n + ENCODED_ELEM_SIZE, # buf - n + ENCODED_ELEM_SIZE) ∧ ( err = ESUCCESS → is-encoded-nonempty (a, subarray(buf, n, ENCODED_ELEM_SIZE)))) subst: [n, a, buf, err, buf0] → [0, a, buf, err, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic