Nuprl Lemma : dl-lt_functionality
∀x,y,x',y':dl-Obj(). ((↑dlo_eq(x;x'))
⇒ (↑dlo_eq(y;y'))
⇒ x ≤ y = x' ≤ y')
Proof
Definitions occuring in Statement :
dlo_le: a ≤ b
,
dlo_eq: dlo_eq(a;b)
,
dl-Obj: dl-Obj()
,
assert: ↑b
,
bool: 𝔹
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
member: t ∈ T
,
iff: P
⇐⇒ Q
,
and: P ∧ Q
,
squash: ↓T
,
uall: ∀[x:A]. B[x]
,
true: True
Lemmas referenced :
assert-dlo_eq,
dlo_le_wf,
istype-assert,
dlo_eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
applyEquality,
lambdaEquality_alt,
imageElimination,
isectElimination,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed
Latex:
\mforall{}x,y,x',y':dl-Obj(). ((\muparrow{}dlo\_eq(x;x')) {}\mRightarrow{} (\muparrow{}dlo\_eq(y;y')) {}\mRightarrow{} x \mleq{} y = x' \mleq{} y')
Date html generated:
2019_10_15-AM-11_44_06
Last ObjectModification:
2019_04_11-PM-02_12_34
Theory : dynamic!logic
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