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Proof step 9 from proof valid-eraseqp-invalidate (previous step)

apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m < # apebs, m0 < # apebs, valid-eraseq(apebs, q0), valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)) → lref = avhdr.vol × avhdr.leb, ∀ m, apebs, apeb. m < # apebs ∧ valid-eraseq(apebs, q0) → valid-eraseq(apebs[m, apeb], q0) ∨ valid-peb(apeb) ⊦ valid-peb(apeb), (valid-peb(apebs[m, apeb][m0]) → lref = apebs[m, apeb][m0].vidhdr.vol × apebs[m, apeb][m0].vidhdr.leb) ∧ valid-eraseq(apebs[m, apeb], q0)

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 10:
apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), lref = avhdr.vol × avhdr.leb, m0 < # apebs, m < # apebs, valid-eraseq(apebs, q0), valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)) → lref = avhdr.vol × avhdr.leb, ∀ m, apebs, apeb. m < # apebs ∧ valid-eraseq(apebs, q0) → valid-eraseq(apebs[m, apeb], q0) ∨ valid-peb(apeb) ⊦ valid-peb(apeb), (valid-peb(apebs[m, apeb][m0]) → lref = apebs[m, apeb][m0].vidhdr.vol × apebs[m, apeb][m0].vidhdr.leb) ∧ valid-eraseq(apebs[m, apeb], q0)
Proof step 21:
apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 < # apebs, m < # apebs, valid-eraseq(apebs, q0), valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)) → lref = avhdr.vol × avhdr.leb, ∀ m, apebs, apeb. m < # apebs ∧ valid-eraseq(apebs, q0) → valid-eraseq(apebs[m, apeb], q0) ∨ valid-peb(apeb) ⊦ lref = avhdr.vol × avhdr.leb, valid-peb(apeb), (valid-peb(apebs[m, apeb][m0]) → lref = apebs[m, apeb][m0].vidhdr.vol × apebs[m, apeb][m0].vidhdr.leb) ∧ valid-eraseq(apebs[m, apeb], q0)

Rule argument

fma: lref = avhdr.vol × avhdr.leb

Additional information

Used formulas: lref = avhdr.vol × avhdr.leb