Nuprl Lemma : sqequalIffSqle
∀a,b:Base. ((a ~ b) ⇒ ((a ≤ b) ∧ (b ≤ a)))
Proof
Definitions occuring in Statement :
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
base: Base,
sqle: s ≤ t,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
has-value_wf_base,
is-exception_wf,
base_sq,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
divergentSqle,
sqequalRule,
hypothesis,
sqleReflexivity,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_pairFormation,
sqequalIntensionalEquality
Latex:
\mforall{}a,b:Base. ((a \msim{} b) {}\mRightarrow{} ((a \mleq{} b) \mwedge{} (b \mleq{} a)))
Date html generated:
2016_05_13-PM-03_45_54
Last ObjectModification:
2015_12_26-AM-09_58_46
Theory : call!by!value_2
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