[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 73 from proof reduction-is-topred-in-ctxt (previous step)

∀ t'. t0 => t' ↔ (∃ C, t2, t1. context(C) ∧ t0 = C[t2] ∧ t2 =>top t1 ∧ t' = C[t1]), ∀ t'. t1 => t' ↔ (∃ C, t0, t2. context(C) ∧ t1 = C[t0] ∧ t0 =>top t2 ∧ t' = C[t2]) ⊦ t0 _ t1 => t' ↔ (∃ C, t2, t3. context(C) ∧ t0 _ t1 = C[t2] ∧ t2 =>top t3 ∧ t' = C[t3])

User applied rule case distinction

And obtained the following new goals

Proof step 43:
t0 _ t1 => t', ∀ t'. t0 => t' ↔ (∃ C, t2, t1. context(C) ∧ t0 = C[t2] ∧ t2 =>top t1 ∧ t' = C[t1]), ∀ t'. t1 => t' ↔ (∃ C, t0, t2. context(C) ∧ t1 = C[t0] ∧ t0 =>top t2 ∧ t' = C[t2]) ⊦ ∃ C, t2, t3. context(C) ∧ t0 _ t1 = C[t2] ∧ t2 =>top t3 ∧ t' = C[t3]
Proof step 72:
∃ C, t2, t3. context(C) ∧ t0 _ t1 = C[t2] ∧ t2 =>top t3 ∧ t' = C[t3], ∀ t'. t0 => t' ↔ (∃ C, t2, t1. context(C) ∧ t0 = C[t2] ∧ t2 =>top t1 ∧ t' = C[t1]), ∀ t'. t1 => t' ↔ (∃ C, t0, t2. context(C) ∧ t1 = C[t0] ∧ t0 =>top t2 ∧ t' = C[t2]) ⊦ t0 _ t1 => t'

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]