Nuprl Lemma : sqle_trans
∀a,b,c:Base. ((a ≤ b) ⇒ (b ≤ c) ⇒ (a ≤ c))
Proof
Definitions occuring in Statement :
all: ∀x:A. B[x],
implies: P ⇒ Q,
base: Base,
sqle: s ≤ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
sqle-wf,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
sqleTransitivity,
hypothesis,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
Error :inhabitedIsType
Latex:
\mforall{}a,b,c:Base. ((a \mleq{} b) {}\mRightarrow{} (b \mleq{} c) {}\mRightarrow{} (a \mleq{} c))
Date html generated:
2019_06_20-AM-11_19_42
Last ObjectModification:
2018_10_06-AM-09_22_18
Theory : sqequal_1
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