Nuprl Lemma : xxtrans_imp_sp_trans
∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. (trans(T;R) ⇒ trans(T;R\))
Proof
Definitions occuring in Statement :
s_part: E\,
xxtrans: trans(T;E),
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
so_apply: x[s1;s2],
strict_part: strict_part(x,y.R[x; y];a;b),
s_part: E\,
xxtrans: trans(T;E)
Lemmas referenced :
trans_imp_sp_trans
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[T:Type]. \mforall{}[R:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. (trans(T;R) {}\mRightarrow{} trans(T;R\mbackslash{}))
Date html generated:
2016_05_15-PM-00_01_41
Last ObjectModification:
2015_12_26-PM-11_26_02
Theory : gen_algebra_1
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