instantiate backward < backward-is-refine with compose-subset-bot , conrefine-def , conbackward-INV by mapping : astate → astate⊥; : cstate → cstate⊥; : globalstate → globalstate⊥; AOP → [λ i. AOP(i) ^]; COP → [λ i. COP(i) ^]; APROG → [APROG⊥]; CPROG → [CPROG⊥]; ASEM → [ASEM⊥]; CSEM → [CSEM⊥]; ⊗ → [⊗]; ⊗ → [⊗]; ⊗ → [⊗]; ⊗ → [⊗]; ⊗ → [⊗]; ⊗ → [⊗]; ⊗ → [⊗]; ⊗ → [⊗]; ran → [ran]; ran → [ran]; ran → [ran]; dom → [dom]; dom → [dom]; dom → [dom]; ⊗ → [⊗]; ⊗ → [⊗]; ⊗ → [⊗]; ⊗ → [⊗]; ran → [ran]; ran → [ran]; ran → [ran]; dom → [dom]; dom → [dom]; dom → [dom]; ⊗ → [⊗]; ⊗ → [⊗]; ⊗ → [⊗]; ⊗ → [⊗]; AINIT → [AINIT ^]; CINIT → [CINIT ^]; AFIN → [AFIN ^]; CFIN → [CFIN ^]; T → [λ cs⊥, as⊥. (T ^)(cs⊥, as⊥) ∧ (as⊥ ≠ ⊥ → AINV(as⊥ .s)) ∨ cs⊥ ≠ ⊥ ∧ ¬ CINV(cs⊥ .s)]; ⊑ → [⊑]; ⊆ → [⊆]; ⊆ → [⊆]; ⊆ → [⊆]; ⊆ → [⊆]; ⊆ → [⊆]; ⊆ → [⊆]; ⊆ → [⊆]; ⊆ → [⊆]; as → as⊥; as0 → as⊥0; as1 → as⊥1; as2 → as⊥2; cs → cs⊥; cs0 → cs⊥0; cs1 → cs⊥1; cs2 → cs⊥2; gs → gs⊥; gs0 → gs⊥0; gs1 → gs⊥1; gs2 → gs⊥2; aop → aop⊥; aop1 → aop⊥1; aop2 → aop⊥2; cop → cop⊥; cop1 → cop⊥1; cop2 → cop⊥2; asem → asem⊥; csem → csem⊥; r → r⊥; t → t⊥; r1 → r⊥1; t1 → t⊥1; r2 → r⊥2; t2 → t⊥2; cinit → cinit⊥; ainit → ainit⊥; cfin → cfin⊥; afin → afin⊥; cinit1 → cinit⊥1; ainit1 → ainit⊥1; cfin1 → cfin⊥1; afin1 → afin⊥1; cinit2 → cinit⊥2; ainit2 → ainit⊥2; cfin2 → cfin⊥2; afin2 → afin⊥2; ap → ap⊥; cp → cp⊥; gp → gp⊥; rename end instantiate